Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity of Hong Kong
Externalities and Property Rights
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Externalities

• Sometimes costs or benefits that result from an
  activity accrue to people not directly involved
  in the activity.
• These are called external costs or external
  benefits -- externalities for short.

3
Example 12.1.

• Sara is an accomplished classical violinist.
• Her neighbor Tom is a fan of classical violin
  music, and on summer evenings enjoys listening to
  Sara play in her garden.
• For Tom, Sara's music is a positive externality.
• If Sara plays only in response to her own costs
  and benefits, will the amount of time she plays
  be socially optimal?

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Example 12.1.

• If Sara plays in response to her own costs and
  benefits, she will continue to play until the
  marginal benefit of playing another minute is
  equal to the marginal cost.
• But since Tom also benefits from her playing, at
  that point the total marginal benefit of playing
  another minute will be greater than the marginal
  cost.

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Example 12.1.

• Thus, if Sara plays in response to her own costs
  and benefits, Sara plays too little.

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Example 12.2.

• Sara is an accomplished classical violinist.
• Her neighbor Harry hates the sound of violin
  music, and on summer evenings becomes distressed
  when Sara plays in her garden.
• For Harry, Sara's music is a negative
  externality.
• If Sara plays only in response to her own costs
  and benefits, will the amount of time she plays
  be socially optimal?

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Example 12.1.

• If Sara plays in response to her own costs and
  benefits, she will continue to play until the
  marginal benefit of playing another minute is
  equal to the marginal cost.
• But since Harry also incurs costs from her
  playing, at that point the marginal benefit of
  playing another minute will be greater than their
  combined marginal costs.

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Example 12.2.

• Thus, if Sara plays in response to her own costs
  and benefits, Sara plays too much.

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Externalities and activity

• Negative externalities gt too much activity
• Positive externalities gt too little activity

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Example 12.3.

• Smith can produce with or without a filter on his
  smokestack.
• Production without a filter results in greater
  smoke damage to Jones.

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Example 12.3.
Smith produces with filter Smith produces without filter
Gains to Smith 200/week 245/week
Damage to Jones 35/week 85/week
If Smith is not liable for smoke damages and if
the two parties can negotiate costlessly with one
another, will he install a filter?
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Example 12.3.
Smith produces with filter Smith produces without filter
Gains to Smith 200/week 245/week
Damage to Jones 35/week 85/week
Total economic surplus goes up if Smith installs
the filter 200-35165 gt 245-85160. The
filter costs 245-20045. Smith doesn't have
to install it, but if Jones pays him at least
45, he will gladly do so. And since the filter
results in savings of 84-3550 for Jones, he
will pay Smith to install the filter.
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The Coase Theorem
If property rights are fully assigned and if
people can negotiate costlessly with one another,
they will always arrive at efficient solutions to
problems caused by externalities.
Ronald Coase 1991 Nobel Laureate in Economics
Additional readings Posner, Richard A. (1993)
Nobel Laureate Ronald Coase and Methodology,
Journal of Economic Perspectives, 7(4)
195-210. Of Bees and Lighthouses Schools
Brief, The Economist, Feb 23, 1991, p.72.
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Example 12.3.

• Traditional (pre-Coase) view
• Smith is the perpetrator (the person who
  committed a crime), Jones is the victim.
• If it is Smith's smoke that is causing the damage
  to Jones, why should Jones pay Smith to install a
  filter on his smokestack?

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Example 12.3.

• Coases insight was that externalities are purely
  reciprocal.
• The smoke harms Jones, true enough.
• But to restrain Smith from producing smoke would
  harm Smith.
• The two parties have a shared interest in
  achieving the outcome that is least costly
  overall.

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Benefit to all when the pie is larger
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Example 12.4.
Ted and Bill can live together in a two-bedroom
apartment for 500/mo
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Example 12.4.
or each rent a one-bedroom apartment for 300/mo.
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Example 12.4.
If the rent were the same, they would be
indifferent between living together or
separately, except for one problem
Ted likes to practice his trumpet late at night
and this will disturb Bill's sleep.
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Example 12.4.

• Ted would pay up to 150/mo rather than
  reschedule his playing.
• Bill would pay up to 80 per month not to have
  his sleep disturbed.
• Will they live together or separately?

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Example 12.4.

• The question is whether the benefits of joint
  living exceeds the costs.
• The benefit is the 100 per month reduction in
  rent.
• What is the least costly accommodation to the
  trumpet problem?

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Example 12.4.

• If they live together
• Cost to Ted of stopping playing 150/mo
• Cost to Bill of tolerating the noise 80/mo
• So the least costly solution is for Bill to put
  up with the noise (since 80 lt 150).
• Since this cost (80) is less than the 100/mo
  gain, they should live together.

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Example 12.5.

• In the preceding example, what is the largest
  rent Bill would be willing to pay if the two were
  to live together?

If Bill were to live alone, he would pay 300/mo
and suffer no trumpet noise. Since the noise
costs him 80/mo, the most he would be willing to
pay for the shared apartment is 300 - 80
220.
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Example 12.6.

• How should Ted and Bill split the 500/mo rent if
  they agree that each should benefit equally from
  living together?

Their total gain from living together is 100 -
80 20/mo. If Ted pays 290/mo and Bill pays
210/mo, each will be 10/mo better off than if
he were to live alone.
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Costly negotiations

• It is often impractical to negotiate solutions to
  the problems created by externalities.
• Hospital patients, for example, are unable to
  negotiate with passing motorists about not
  blowing their horns.
• In such cases, the law tries to impose the burden
  of adjustment on the party that can accomplish it
  at lowest cost.

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Costly negotiations
Not blowing his horn is a cost to the motorist,
but a benefit to the patient. Because peace
and quiet is especially valuable for hospital
patients, the law prohibits horn blowing in the
vicinity of hospitals.
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Costly negotiations
In non-hospital zones, the law is more liberal in
its tolerance of noise. In many cities, there
are 11 PM noise curfews on weekdays, midnight
curfews on weekends.
For those who are interested in law and
economics Bouckaert, Boudewijn and De Geest,
Gerrit (eds.), Encyclopedia of Law and Economics,
Cheltenham, Edward Elgar, 2000
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Example 12.7. The Right to an Unobstructed View

• Lehman owns a house overlooking the lake, from
  which he enjoys a commanding sunset view.

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Example 12.7. The Right to an Unobstructed View

• Now Martin purchases the property below Lehman's
  and is considering which of two houses to build
  
• a one-story house that would leave Lehman's view
  intact
• or a two-story design that would completely block
  Lehman's view.

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Example 12.7. The Right to an Unobstructed View

• Suppose the gain to Lehman from an unobstructed
  view is 100, the gain to Martin from having a
  one-story house is 200, and the gain to Martin
  from a two-story house is 280.
• If the laws of property let people build houses
  of any height they chose, and if negotiation
  between property owners were costless, which of
  the two houses would Martin build?

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Example 12.7. The Right to an Unobstructed View

• Value of view to Lehman 100
• Value of second story to Martin 280-20080
• The increase in Martin's gain from having the
  taller house is 80, which is 20 less than the
  cost to Lehman from the loss of his view.
• The efficient outcome is thus for Martin to build
  the one-story house.
• And that is exactly what would happen if the two
  parties could negotiate costlessly.

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Example 12.7. The Right to an Unobstructed View

• Rather than see Martin build the taller house, it
  will be in Lehman's interest to compensate Martin
  for choosing the shorter version.
• To do so, he will have to give Martin at least
  80.
• The most Lehman would be willing to pay is 100,
  since that is all the view is worth to him.
• For some payment P, where 80?P?100, Lehman will
  get to keep his view.

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Example 12.7. The Right to an Unobstructed View

• Suppose, however, that negotiations between the
  two parties were impractical.
• Martin would then go ahead with the two-story
  house, since that is the version he values most.
  
• By comparison with the one-story design, Martin
  would gain 80, but Lehman would lose 100.
• The optimal structure of property rights in this
  particular example would be to prohibit any
  building that blocks a neighbor's view.

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Example 12.7. The Right to an Unobstructed View

• If the valuations assigned by the parties were
  different, a different conclusion might follow.
• If, for example, Martin valued the two-story
  house at 300 and Lehman valued the view at only
  80, the optimal structure of property rights
  would be to allow people to build to whatever
  height they chose.

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Modified Coase Theorem

• The optimal structure of property rights is the
  one that places the burden of adjustment (either
  the loss of a view or the loss of a preferred
  building design) on the party that can accomplish
  it at the lowest cost.
• As a practical matter, the laws of property in
  many jurisdictions often embody precisely this
  principle.

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Modified Coase Theorem

• In cities like San Francisco, strict zoning laws
  prohibit construction that blocks an existing
  building's line of sight

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Modified Coase Theorem

• Zoning laws in cities where there is less to look
  at are generally much more liberal in the kinds
  of buildings they permit.

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Modified Coase Theorem

• But even in cities that have no special view to
  protect at all, zoning laws generally limit the
  fraction of the lot that can be occupied by
  manmade structures.

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Example 12.8. Taxing Negative Externalities

• Two firms, X and Y, have access to five different
  production processes, each one of which has a
  different cost and gives off a different amount
  of pollution.

Process (daily smoke) A (4 tons) B (3 tons) C (2 tons) D (12 tons) E (0 ton)
Cost to Firm X 200 290 700 1300 2100
Cost to Firm Y 50 80 140 230 325
If pollution is unregulated, and negotiation
between the firms and their victims is
impossible, each firm will use A, the least
costly of the five processes. Each will emit 4
tons of pollution per day, for a total pollution
of 8 tons/day.
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Example 12.8. Taxing Negative Externalities

• The city council wants to cut smoke emissions by
  half. To accomplish this, they are considering
  two options.
• Require each firm to curtail its emissions by
  half.
• Set a tax of T on each ton of smoke emitted each
  day.
• How large would T have to be in order to curtail
  emissions by half?
• And how would the total costs to society compare
  under the two alternatives?

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Example 12.8. Taxing Negative Externalities

• A If each firm is required to cut pollution by
  half, each must switch from process A to process
  C.
• The result will be two tons/day of pollution for
  each firm.

Process (daily smoke) A (4 tons) B (3 tons) C (2 tons) D (1 tons) E (0 ton)
Cost to Firm X 200 290 700 1300 2100
Cost to Firm Y 50 80 140 230 325
The cost of the switch for firm X will be
700/day-200/day500/day. The cost to Y will
be 140/day-50/day90/day, So total cost for the
two firms 590/day.
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Example 12.8. Taxing Negative Externalities

• B How will each firm respond to a tax of T per
  ton of pollution?
• Switching to the next process will cut pollution
  by 1 ton per day and save tax of T/day.
• If cost of switching to the next process is less
  than or equal to T, it will switch, otherwise not.

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Example 12.8. Taxing Negative Externalities

• T 50/ton Firm X would stick with process A.
  Firm Y will switch to process B.

Process (daily smoke) A (4 tons) B (3 tons) C (2 tons) D (1 tons) E (0 ton)
Cost to Firm X 200 290 700 1300 2100
Cost to Firm Y 50 80 140 230 325
A tax of 50/ton thus does not produce the desired
50 percent reduction in pollution.
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Example 12.8. Taxing Negative Externalities

• T 91/ton. X will adopt process B, Y will adopt
  process D.

Process (daily smoke) A (4 tons) B (3 tons) C (2 tons) D (1 tons) E (0 ton)
Cost to Firm X 200 290 700 1300 2100
Cost to Firm Y 50 80 140 230 325
Total emissions will be the desired 4 tons/day.
Cost to firm X will be 290/day-200/day 90/day.
Cost to firm Y will be 230/day-50/day 180/day.
Total cost for both firms is thus only 270/day,
or 320/day less than the cost of having each firm
cut pollution by half.
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Example 12.8. Taxing Negative Externalities

• Note that the taxes paid by the firm are not
  included in our reckoning of the social costs of
  the tax alternative, because this money is not
  lost to society.
• It can be used to reduce whatever taxes would
  otherwise have to be levied on citizens.

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Example 12.9. Pollution Permits

• Similar to the preceding example but now the
  government issues pollution permits to the two
  firms, allowing them to generate 4 tons of smoke
  daily, in total.
• Will the pollution generated by the two firms
  change with the different allocation of permits?

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Example 12.9. Pollution Permits

• Similar to the preceding but now the government
  issues pollution permits to the two firms,
  allowing them to generate 4 tons of smoke daily,
  in total.
• Suppose each firm is given permits to generate 2
  tons of smoke.

Process (daily smoke) A (4 tons) B (3 tons) C (2 tons) D (1 tons) E (0 ton)
Cost to Firm X 200 290 700 1300 2100
Cost to Firm Y 50 80 140 230 325
By moving from C to B, Firm X will generate 1
more ton of smoke but will save a cost of 410.
By moving from C to D, Firm Y will incur a cost
of 90. Negotiation will ensure the new
allocation (3 tons for firm X, and 1 ton for firm
Y)
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The Tragedy of the Commons
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Example 12.10

• A village has five residents, each of whom has
  accumulated savings of 100.
• Each villager has two investment opportunities
• Buy government bond for 100 that pays 12
  interest per year.
• Buy a year-old steer for 100, send it onto the
  commons to graze, then sell it after one year.

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Example 12.10

• The Relationship Between Herd Size, Selling
  Price, and Profit per Steer

Number of steers on the commons Price per 2-year- old steer () Profit per steer ()
1 120 20
2 116 16
3 114 14
4 112 12
5 110 10
If each person decides individually how to
invest, how many steers will be sent onto the
commons?
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Example 12.10
If each person decides individually how to
invest, how many steers will be sent onto the
commons?
Number of steers on the commons Price per 2-year- old steer () Profit per steer ()
1 120 20
2 116 16
3 114 14
4 112 12
5 110 10

• Opportunity cost of investing in steer 12
• Send steer if and only if price of 2-year-old
  steer is at least 112
• Four of the villagers send 1 steer, and hence a
  total of 4 steers.
• Total village income 12 4(12) 60

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Example 12.10
In the preceding example, what is the socially
optimal number of steers?
Number of steers on the commons Price per 2-year- old steer () Value of herd ()
1 120 120
2 116 232
3 114 342
4 112 448
5 110 550

• Decision rule for socially optimal
  investmentSend another steer only if the value
  of the herd increases by at least 12.
• Thus, we should send a second steer but not a
  third. Total income 32 36 68

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Tragedy of commons

• The problem with private decisions is that no
  individual has any incentive to take into account
  that an extra steer will eat grass that otherwise
  would have been available to the steers already
  on the commons.
• The tragedy of the commons is thus a type of
  externality.

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Example 12.11.

• Sam and Stan are identical twins with a craving
  for chocolate malted milkshakes, and have agreed
  to share one.

If each has a straw and each knows that the other
is self-interested, will the rate at which they
consume the milkshake be optimal?
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Example 12.11.

• Each knows that any part of the milkshake he
  doesn't drink will be drunk by the other.
• So each consumes at a faster rate than he would
  if he had half the shake all to himself.

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Examples of Tragedies of the CommonsHarvesting
timber on public land.
Each tree cutter knows that a tree not harvested
this year will be bigger, and hence more
valuable, next year. But he also knows that if
he doesn't cut the tree down this year, someone
else will.
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Examples of Tragedies of the Commons Picking
blackberries in a public park
Each individual knows that the blackberries would
taste better if allowed to ripen for another
week. But each also knows that blackberries
not eaten today may not be there next week.
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Examples of Tragedies of the CommonsHarvesting
whales in international waters
Each individual whaler knows that harvesting an
extra whale reduces the breeding population of
whales and hence the size of future whale
populations. But he also knows that any whale
he fails to harvest today will just be taken by
some other whaler.
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Examples of Tragedies of the CommonsPollution
Each individual polluter has no incentive to take
into account the cost his pollution imposes on
others.
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Tragedies of the Commons

• Clearly defined property rights are one way to
  solve the tragedy of the commons

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Example 12.12. (Chapter 1-4)

• Once a week, Smith purchases a six-pack of cola
  and puts it in his refrigerator for his two
  children. He invariably discovers that all six
  cans are gone on the first day. Jones also
  purchases a six-pack of cola once a week for his
  two children, but unlike Smith, he tells them
  that each may drink no more than three cans. If
  the children use cost-benefit analysis each time
  they decide whether to drink a can of cola,
  explain why the cola lasts much longer at Jones
  house than at Smiths.

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Example 12.12. (Chapter 1-4)

• At Smiths house, each child knows that the cost
  of not drinking a can of cola now is that it is
  likely to end up being drunk by his sibling. Each
  thus has an incentive to consume rapidly to
  prevent the other from encroaching on his share.
  
• Jones, by contrast, has eliminated that incentive
  by making sure that neither child can drink more
  than half the cans. This step permits his
  children to consume at a slower, more enjoyable
  pace.

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Defined property rights as a solution to tragedy
of the commons
Weyerhauser doesn't cut trees down too quickly on
its own land.
Weyerhaeuser is an international forest products
company with annual sales of 22.6 billion. It
was founded in 1900 and currently employs about
54,000 people in 18 countries.
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Defined property rights as a solution to tragedy
of the commons
People don't harvest blackberries too soon from
their backyard garden.
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Defined property rights as a solution to tragedy
of the commons
People don't dump toxic wastes into their own
swimming pools.
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Regulation as a solution to tragedy of the commons
Fishing licenses limit the amount of fish that
can be taken.
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Regulation as a solution to tragedy of the commons
Laws regulate air and water pollutants.
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Regulation as a solution to tragedy of the commons
Zoning laws limit the size and other features of
buildings, signs, land-use patterns, etc.
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Regulation as a solution to tragedy of the commons
Mandatory recycling
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Example 12.13

• In the cattle-grazing economy considered earlier,
  suppose there is now a 25 tax on income earned
  from cattle.
• If people decide individually between bonds and
  cattle, how many steers will be sent onto the
  commons?

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Example 12.13
With a 25 tax on income from cattle, only 2
steers will be sent onto the commons, and this is
the socially optimal number.
Number of steers on the commons Price per 2-year- old steer () After-Tax Profit per steer (), with 25 tax on cattle income
1 120 15
2 116 12
3 114 10.50
4 112 9
5 110 7.50
Total income 3(12) 2(12) 8
68 (bonds) (cattle) (tax)
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Tragedy of the commons

• One of the continuing sources of inefficiency in
  modern economies involves the allocation of
  resources that no single nation's property laws
  and regulations can govern.
• Several species of whales have been hunted to
  near extinction because international laws of
  property are insufficient to restrain individual
  incentives to kill whales.
• The Mediterranean Sea has long had serious
  problems with pollution, because none of the many
  nations that border it has an economic incentive
  to consider the effects of its discharges on
  other countries.

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Example Why do football players take anabolic
steroids?

• Smith and Jones are competing for a single
  position and a 1 million contract.

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Example Why do football players take anabolic
steroids?
Jones
Dont take steroids
Take steroids
Second best for each Best for Jones Worst for Smith
Best for Smith Worst for Jones Third best for each
Dont take steroids
Smith
Take steroids

• Dominant strategy for each yields the third best
  outcome
• This prisoners dilemma outcome is the attraction
  of rules banning performance enhancing drugs.

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Positional Arms Races and Positional Arms Control
Agreements

• Positional Externality
• When an increase in one persons performance
  reduces the expected reward of another in
  situations in which reward depends on relative
  performance
• Positional Arms Race
• A series of mutually offsetting investments in
  performance enhancement that is stimulated by a
  positional externality

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Positional Arms Races and Positional Arms Control
Agreements

• Positional Arms Control Agreements
• An agreement in which contestants attempt to
  limit mutually offsetting investments in
  performance enhancements
• Campaign spending limits
• Roster limits
• Arbitration agreements
• Mandatory starting dates for kindergarten

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Positional Arms Races and Positional Arms Control
Agreements

• Social Norms as Positional Arms Control
  Agreements
• Nerd norms
• Good grades vs. all study too hard
• Fashion norms
• Avant-garde status vs. excessive body mutilation
• Norms of taste
• Catching attention vs. too much nudity
• Norms against vanity
• Cosmetic/reconstructive surgery vs. Michael
  Jackson

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End