Can Markets Set Caps for
Cap-and-trade
Pollution Permits?
Ted Bergstrom
Economics Department
University of California Santa
Barbara
Alternate Title:
Arrow, Coase, Missing Markets,
and the Easter Bunny
Economists have lots of good
ideas that politicians and public
don’t like as well as we do.
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•
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•
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Gasoline Tax
Congestion Tolls
Legalize and tax recreational drugs
Legalize trade in body organs
Subsidize surstrőmming?
Tradable pollution permits: an
economists’ idea that got popular
• Endorsed by Clinton, Edwards, Obama,
and McCain
• By major energy companies
• Some Environmental Groups
– Environmental Defense Fund, Union of
Concerned Scientists
– But not Sierra Club
A Coasian Solution to
Externalities?
• A fond hope of many economists is that
externalities can be internalized by
establishing property rights and market
institutions.
• Achieved with a minimum of government
regulation.
• Reduce politicians’ chances for corruption
and bribery.
• Is this Easter Bunny economics?
What is cap-and-trade?
• Government requires a permit for every unit
of pollution produced.
• Issues a fixed number of tradable permits.
• Permits typically issued to original polluters
in proportion to historic pollution.
– Wouldn’t have to be this way. Could be
auctioned.
• Number of permits decreases over time.
Los Angeles Air Quality
• Typical example: Southern California’s
RECLAIM market started in 1992.
– Tradeable permits for SOx and NOx issued to
large polluters in L.A. in proportion to
emissions they produce at full capacity.
– Number of permits issued reduced by 8% per
year 1992-2003.
• Large brokerage firms handle trades
– Coasian Transaction costs? Commissions: 1-3.5 percent
• L.A. air quality has improved drastically.
Other Cap-and-trade markets
• Acid Rain SOx markets in Eastern US
States
• Water pollution in Wisconsin and
Colorado
• Fisheries in Australia and New Zealand
• Tradable permits to own cars in Singapore.
– Number increases by 3% per year.
– New permits auctioned in “Walrasian
auction”
Alternatives to Cap-and-Trade
• Command and control measures
• Pigovian Pollution tax
• Why do energy companies like cap-andtrade?
– Preferable to C and C or pollution tax if they
get the permits.
– Especially if abatement technologies are
cheaper for them than for others.
Advantage of Cap-and-Trade
• Decentralizes firms’ decisions about whether
to install abatement devices, change
technologies, cut back output, move away.
• Marginal benefits from polluting are about
the same* across all firms and equal to
marginal costs of abatement.
• Conditional on aggregate level of pollution,
if market is competitive, outcome is Pareto
efficient.
Further advantage
• Endowing current polluters, reduces
opposition, makes change nearly Pareto
improving
– Except for grouchy people at Sierra Club
• Even grouches may concede that they
need to buy off polluters to get reform.
What is missing
• Cap-and-trade policies do a good job of
allocating chosen level of cap, but cap is
currently chosen by political bodies.
• Can the caps also be determined by
markets?
Arrow’s suggestion
• Arrow (1969) stated:
“By a suitable and not unnatural
reinterpretation of the commodity space,
externalities can be regarded as ordinary
commodities and all of the formal theory
of competitive equilibrium is valid,
including its optimality”
Arrow’s formalism
• Treat pollution of each victim as a
separate commodity.
• These are joint products of pollutant
produced by a polluter.
• Competitive equilibrium would exist in
this imaginary economy and would be
the same as a Lindahl equilibrium, which
would be Pareto optimal.
Does this mean that
decentralized markets can
optimize externalities ?
Not so fast, says Arrow
• The existence of Lindahl equilibrium prices
for pollution does mean that they can be
implemented in a working market.
• Two problems.
– 1) Free-riders cannot be excluded from
benefits of air quality purchased by others.
– 2) Personalized markets are thin markets.
Competitive outcome is unlikely.
Do Arrow’s 2 problems doom a
full market solution for
pollution control methods?
• Rays of hope from mechanism design.
– Weakly dominant Groves Clarke Mechanism
– Nash implementation
• Groves-Ledyard
• Mark Walker and others
• Not like markets, but maybe some kind of
market will work.
Is there a way around these
problems?
Multiple polluters, single victim
• Assume there are many firms, each produces
a single pollutant as a bi-product and could
reduce the ratio of pollutant to output at
some cost.
• There is only one pollution victim.
• Government monitors pollution and requires
a permit for each unit of pollutant emitted.
• Government issues enough permits for total
pollution produced before permits required.
Permits given to Polluters
• Government issues permits to original
polluters equal to their previous emissions.
• Pollution victim can buy permits and retire
them.
• Outcome will be efficient and Pareto superior
to status quo ante.
• Damage to victim of marginal unit of
pollution equals marginal benefit of polluting
and marginal cost of abatement for each
polluter.
Permits given to victim
• We may think that the victim had a right
to a clean environment and should not
have to pay.
• Coasian argument : No worries. Just
endow the victim with the permits.
Outcome will be the same except for
income distribution.
Not so fast, Mr. Rabbit
• Victim will now be a monopoly seller of
permits.
• Marginal cost of selling a permit is victim’s
disutility of pollution.
• Firms’ demand for permits will be
downward sloping. Marginal revenue will
exceed price.
• Victim will sell too few permits for efficiency.
We could use a Pigovian tax, but how high
should the tax be set?
Many Polluters, Many Victims
• Assume many polluters as before, but now
let there be many pollution victims.
• Suppose that pollution permits are required
and permits issued to current polluters
allowing pre-permit pollution levels.
• This establishes property rights to air quality.
Victims can buy and retire permits. Markets
give us efficiency, right?
Not so fast, Mr. Rabbit
• Nash equilibrium in this market will be the
voluntary provision of public goods outcome.
• The equilibrium price in this market will be
equal to the marginal cost of pollution to any
individual victim who buys tickets.
• Each retired premit reduces pollution for all
victims, yet purchasers consider only their own
gains.
• Efficiency requires price of permit equals sum
of marginal costs to victims. Equilibrium has
far lower price, equal to maximum of marginal
costs to victims.
Endowing the victims
• Can we cure the problem by endowing the
victims rather than the polluters?
• Suppose the total supply of permits was
divided equally among victims. Market
would be competitive now: many victims
• Victims would be willing to supply at their
marginal damage. Equilibrium price would
be marginal damage to a single person.
Again far below efficient price. And total
revenue received by victims far less than total
damage caused by pollution.
Personalized permits
• Suppose that the government endows
each pollution victim a number of
pollution permits equal to the total
amount of pollution produced before
permits were introduced.
• For each unit of pollution that a firm
produces, it must have one personalized
permit from each victim.
Unanimous consent?
• What goes wrong when many victims are
endowed with tradable permits?
• Each victim can sell permission to pollute not
only himself but everyone in the community.
• Lets try market devices that require unanimous
(or near unanimous consent) of victims.
• (Wicksell suggested that near unanimity might
be required for tax-funded projects.)
Too many commodities?
• Think of a global market with a small
number of nations acting on behalf of their
citizens. Polluters need a permit from each
country for each unit of pollution they
produce.
Complementary monopoly
problem
• Each victim is the monopoly supplier of his
own permits.
• Permits are perfect complements.
• This is the complementary monopoly model
of Cournot.
• Output is even smaller than with a single
monopoly.
– Total markup as percentage of sum of prices is
N/|E|, where E is elasticity of demand and N
the number of victims.
Fixing Arrow’s Problem 2
• We could have personalized permits
without monopoly by spreading initial
endowments of each victim’s permits
among many participants
– either victims or polluting firms, depending
on distributional goals.
• There would be many demanders for
these permits—several firms and one
victim.
Lindahl equilibrium
• Endowment of X personalized permits for each
person is distributed.
• In equilbrium, each victim buys the same quantity
Q of his own permits and firms buy a total of X-Q
of each kind of permit.
• Each person’s personalized price is his marginal
rate of substitution between pollution and private
goods.
• Cost to a firm of producing a unit of pollution is
sum of prices of personalized permits.
Can we implement Lindahl with
competitive permit market?
• The Lindahl equilibrium would be a
competitive equilibrium if each victim
experienced X-Qi units of pollution when
he retires Qi permits.
• But in the actual market we have
proposed, firms can only produce
X-max{Qj} units of pollution.
Competitive equilibrium doesn’t
exist.
But is there some other kind of
equilibrium and is it any good?
Hope springs eternal
Had enough?