Externalities

Econ 325 Martin Farnham

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Externalities--Introduction •  Externalities occur when some market

transaction involves costs and/or benefits that accrue to people outside the transaction –  Consumers weigh up the costs and benefits to

themselves of engaging in a transaction; we call these private costs and benefits

–  Producers weigh up the costs and benefits to themselves of engaging in a transaction (these are also private costs and benefits)

–  But neither consumers nor producers are likely to weigh the costs or benefits to others affected by a transaction

•  We call costs or benefits experienced by people outside the transaction external costs or external benefits or (generally) externalities.

Externalities--Introduction

– When costs or benefits are experienced by people outside a transaction, the actors in the transaction (consumers and producers) don’t take those external costs or benefits into account.

– The choices of private actors to maximize consumer and producer surplus may not lead to overall maximization of net benefits (because external costs and benefits are ignored by economic actors)

–  In such a case, equilibrium is inefficient 2

Externalities--Introduction •  Externalities can occur in production or

consumption •  Externalities can be positive or negative

On Which Side is Externality? Production Consumption

Negative Pulp-mill pollution smoking; loud music

Positive R&D spillovers, Bee keeping

Painting house; gardening 3

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Externalities--Introduction •  Some more examples:

–  Positive Consumption externalities •  Your attending party may add to festive atmosphere for

others –  Negative Consumption externalities

•  Sitting in class eating stinky food, wearing strong perfume, or cracking gum

–  Positive Production externalities •  Firms learn from each other by working in close

proximity; productivity-enhancing ideas spread (knowledge spillovers)

–  Negative Production externalities •  Mining projects may ruin nice vistas, pollute rivers •  Construction creates noise pollution

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If consumers bid up the price of a commodity, is this an externality?

•  Consider an art auction: I value a painting at $1000, you value it at $800

•  We’re the two highest bidders. •  My outbidding you reduces benefits to you by $800.

But I pay that $800 (and more) in outbidding you –  I’m bearing the full cost of depriving you of that benefit –  Not an externality! –  If I lived in the apartment above you and let my bathtub

overflow so it leaked on the painting and destroyed it (and couldn’t be held accountable)--that’s an externality

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Externalities and Social Welfare in S-D Context

•  For efficiency, we need MB=MC – Let’s be more specific: Want marginal

social benefit to equal marginal social cost •  We want the last unit produced to yield benefits

to society (both people engaged in the transaction *and* anyone not engaged but affected by the transaction) that exactly equal the costs to society yielded by the last unit

•  When no externality is present (all costs and benefits are private), marginal social cost is the same as marginal private cost; and marginal social benefit is the same as marg. priv. benefit

Externalities and Social Welfare in S-D Context

•  In equilibrium, MPC=MPB (see review) –  If no externality is present, then MPC=MSC

and MPB=MSB; so in equilibrium (with no externalities), MSC=MSB. equilibrium is efficient.

–  If an externality is present, then either MSC≠MPC or MSB≠MPB (or both); and hence equilibrium (where MPC=MPB) is unlikely to be efficient

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Externalities in S-D Context

•  For the sake of thinking about externalities, let’s be very explicit about the accounting –  Marginal private benefit (MPB)=marginal

willingness to pay (demand curve) –  Marginal private cost (MPC)=marginal cost of

producers (supply curve) –  Marginal external benefit (MEB)=marginal benefit

accruing to outside parties (positive externality) –  Marginal external cost (MEC)=marginal cost

accruing to outside parties (negative externality)

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Externalities in S-D Context

•  Consumption externalities are shown with the MB curve – MSB=MPB+MEB-MEC

•  Production externalities are shown through the MC curve – MSC=MPC-MEB+MEC

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Showing Externalities in S-D Context

•  Spz marginal external benefit of an activity is constant –  Denote with horizontal

MEB curve –  MSB curve will be

vertical shift of D curve by amount of MEB (vertical sum)

–  MSB=MPB+MEB –  MSC=MPC because no

externality on production side

Positive Consumption Externality

D=MPB

S=MPC=MSC

Qeq

Peq

Qeff

P

Q

MEB MSB

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Showing Externalities in S-D Context

•  Now spz constant MEB comes from production activity; show with S curve –  Vertical shift (down) of S

curve by amount of MEB –  MSC=MPC-MEB –  MSB=MPB because no

externality on consumption side

–  Too little produced in equilibrium

Positive production externality

D=MPB=MSB

S=MPC

Qeq

Peq

Qeff

P

Q

MEB MSC

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Note that MEC or MEB need not be constant

•  Could be increasing •  Could start above zero

D=MSB

S=MPC MSC

Qeq

Peq

Qeff

P

Q

D=MSB

S=MPC

MSC

Qeq

Peq

Qeff

P

Q

MEC

MEC

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Consider a negative production externality (MEC>0)

•  Equilibrium at Qeq where S=D

•  But is this efficient? –  MSC=MPC+MEC –  MSC>MSB at Qeq implies

that too much is being produced

–  Want MSC=MSB –  Qeff is efficient level of

production D=MSB

S=MPC

MSC

Qeq

Peq

Qeff

P

Q

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Negative Production Externality

•  Without a market intervention, too much of this good will be produced.

•  How do we know it’s too much? –  MSC>MSB in equilibrium; this means we could

reduce production by a little bit, and have social welfare increase

–  Thus social welfare is not maximized in equilibrium •  Let’s do the welfare analysis to prove this

Neg Prod Externality--Welfare Analysis

•  Social welfare (aggregate net benefits) in equilibrium –  Add up all benefits at

Qeq, subtract all costs at Qeq.

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Neg Prod Externality--Welfare Analysis

•  With negative production externality and no government intervention,

•  SW=(total benefits) – (variable costs + total external costs)

•  Alternatively SW=(triangle A) – (triangle B) •  Alternatively SW=CS+PS-TEC

–  TEC: total external costs

•  SW could actually be negative or zero (though not in this case, judging from relative areas)

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Neg Production Externality--Welfare Analysis

•  What does society gain from moving from Qeq to Qeff? –  Loses total social

benefits of E –  Gains total social cost

reduction equal to D –  Net gain of F –  Note that F is equilibrium

deadweight loss –  Welfare society could

have if only it moved from Qeq to Qeff.

D=MSB

S=MPC

MSC

Qeq

Peq

Qeff

P

Q

E

D

=gain loss=

F

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Note the Opportunity to Pay Off Producers/Consumers

•  Take last unit produced in equilibrium –  No gain to firm or

consumers (Marginal Producer Surplus=0; Marginal Consumer Surplus==0)

–  Big MEC to others –  Could pay producers +

consumers anything greater than 0 to convince it not to produce/consume last unit

–  Coordination problem if many people/firms involved.

D=MSB

MSC

Peq

P

Q Qeq Qeff

S=MPC

MEC

MPS

For all Q between Qeff and Qeq, MEC≥MPS+MCS

MCS

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This Points to A Couple Ways To Induce Polluter to “Do the Right Thing”

1) Pay polluter not to pollute. –  e.g. payment equal to MEC for each unit reduced

from Qeq

2) Charge the polluter for polluting –  Impose a tax in order to reduce level of the

polluting activity 3) Convince yourself that these are equivalent.

–  A $5 per unit tax raises the opportunity cost of each unit produced by $5.

–  A $5 per unit reward for not producing raises the opportunity cost of each unit produced by $5

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Aside: Effect of a per unit tax on output (assume no externality)

•  Suppose we force suppliers to pay a per unit tax of $t –  Shifts up firms’

“willingness to accept” curve (Supply)

–  If they try to pass all of t on to consumers, will be faced with excess supply.

–  Forces consumer price to fall; so producer price falls too: Ps=Pc-t

•  Per unit tax imposed on market

Peq

P

Q Qeq Q’eq

D

S

S(w/tax)

t Peq+t

Excess S

Pc

Ps

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Welfare Effects of a per unit Tax (no externality case)

•  Suppose original equilibrium was efficient –  Social welfare is

maximized without intervention

–  Tax can only make things worse

•  Social welfare without tax

Peq

P

Q Qeq

D

S CS

PS

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Welfare Effects of a per unit Tax (no externality case)

•  SW=CS+PS+GR –  GR: govt revenue –  GR=t·Q’

•  Note that SW has declined, due to the reduction in quantity –  Some CS was lost

without being recaptured as GR

–  Some PS was lost without being recaptured as GR

–  Lost CS+Lost PS = DWL

•  Social Welfare with tax

Peq

P

Q Qeq Q’eq

D

S

S(w/tax)

t Pc

Ps

CS

PS

Govt Revenue

DWL

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Using a per unit tax to correct an externality

•  Tax is SW reducing for market success

•  Tax can be SW improving for mkt failure –  w/neg externality, can

restore Qeff –  Impose tax that sets

t=MEC at Qeff •  SW after tax equals

areas CS+PS+GR-TEC •  Notice that the efficient

quantity involves positive amounts of the externality.

CS= GR= PS=

MSC

Peq

P

Q Qeq

S=MPC

Q’eq=Qeff

S(w/tax) t=MEC(Qeff)

Pc

Ps

TEC=

D=MSB

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SW With Tax-Corrected Externality

•  Social welfare in this case is the area shown to the right. –  It’s CS plus the part

of GR not cancelled out by TEC.

–  Note that PS is cancelled out by part of TEC

•  Social Welfare

=

SW CS+GR+PS

- TEC

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To Impose Correct Tax, Need to be able to measure MEC

•  Easier said than done! –  Spz only one firm pollutes

•  Still need to be able to measure external effects of pollution

•  How much damage in dollar terms does it really cost? –  Very difficult to find out –  Could conduct surveys, but people don’t have incentive to

tell truth; might need to develop means to induce people to reveal their true valuation of the damages

–  Could try to infer value some other way (e.g. compare house prices in polluted vs. non-polluted areas; compare health outcomes/medical costs in polluted vs. non-polluted areas)

–  Now suppose many firms pollute: hard to assign damages if different firms pollute different amounts

•  Need meters on smokestacks, etc.

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Externalities--Other Potential Solutions

•  Other government interventions •  Private market solutions

– Assign property rights and allow bargaining between players •  Coase Theorem

– Find other way to “internalize” externality •  e.g. Have the apple grower buy the beekeeping

business – Create market for the externality

•  e.g. Tradeable pollution permits

Other Government Interventions to Solve Externality Problem

•  Command and control –  Govt could just tell firms which quantity to

produce; how to produce (pollution standards) •  Taxes or subsidies

–  Neg externality: too much produced in equilibrium, so tax it.

–  Positive externality: too little produced in equilibrium, so subsidize it.

•  Price controls –  Govt could set price at level that induces

production of efficient quantity •  Quantity controls

–  Govt could set quota at efficient quantity •  Won’t work for positive externality. Why? 27

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Private Solutions--Coase Theorem

•  The fundamental problem with externalities is a lack of assigned property rights

•  Take case of a river with two users (upstream and downstream) –  Upstream user values river as place to dump

factory outflow –  Downstream user values river for clean water and

fishing –  If neither owns the river, externality likely to be a

problem

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Coase Theorem

•  Without clear property rights, upstream user will dump waste in river, not taking into account effect on downstream user –  River will be “too” polluted –  Could give river to upstream user

•  Let upstream user pollute; downstream user can pay upstream user to pollute less

•  Will do so if MEC>(MB-MPC) –  MEC>Producer and consumer surplus on the margin

•  River will end up as clean as downstream user is willing to pay for

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Coase Theorem

–  Could give river to downstream user •  Upstream user could pay downstream user for right to

pollute to some agreed-upon level •  Will do so as long as (MB-MPC)>MEC •  River will end up as polluted as upstream user is willing

to pay for –  Regardless of who we give the property rights, the

outcome will be the same (and will be efficient) •  Overall SW will be the same •  Individual welfare will differ, depending on who gets

given the river

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Problems with Coase Theorem

•  Coase Theorem is difficult to implement in practice –  Requires small number of players (need zero

bargaining costs to work perfectly) •  Good for solving roommate issues over smoking, loud

music, etc.; neighbors resolving conflicts –  Must be able to identify the source of damages

•  (costless monitoring) –  What if thousands of people fish in the river?

Hundreds of firms pollute it? –  How do you assign property rights to air?

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Problems with Coase Theorem •  Textbook cites example of Zimbabwe giving

elephant herds to local villagers –  They can hunt them if they want –  They can preserve them (selectively harvest--

typically by selling right to hunt one to Texas oil barons or rich internet hunters)

–  But what if herd migrates onto someone else’s land? What if it trashes a farmer’s crops (village could compensate farmer?).

–  Probably not as clean a case as textbook makes out, but maybe worth a try

–  For a fairly free market perspective, see http://www.econlib.org/library/Enc1/PublicGoodsandExternalities.html

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Private Solutions--Mergers

•  Take a beekeeper located next to an apple orchard (2 different firms) –  Spz costs of apple production are decreasing in

the number of bees –  Beekeeper doesn’t take this into account –  Apple producer could pay beekeeper to keep more

bees (Coase) –  Or apple producer could buy the beekeeper’s firm,

and operate both as one firm. •  This “internalizes” the externality. Now the firm will take

into account all benefits (and costs) of beekeeping •  Leads to efficient production (if apple orchard was only

outside party affected by beekeeping)

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Private Solutions--Social Conventions

•  One way to manage externalities is to stigmatize actions that lead to them –  Example: politeness

•  Sometimes its inconvenient to be polite, but we’re taught from a young age to be civil to others, even when we have nothing to gain from it

•  There’s an externality associated with politeness; if you don’t cut someone off in traffic, that person and possibly others will be happier for it

•  By frowning on impolite behaviour, society (through social institutions/norms/conventions) manages an activity with an externality

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Social Conventions •  Cowardice is a problem in military settings (if

everyone in a unit always ducks, the unit will get wiped out) –  Hence medals for heros –  Shame (or worse) for cowards

•  Problems with using social norms to manage externalities –  No guarantee you’ll get the efficient level of courage,

politeness, etc. –  Enforcing social norms is subject to a free-rider problem

(we’ll talk more about this with public goods) –  Social norms don’t collect revenues. Taxes do! –  The beauty of using taxes to deal with negative externalities

is that you solve a market failure *and* get revenues while doing it! Much nicer outcome for society than just forcing people to “behave well”

Tradeable Permits—A market based alternative to a pollution tax

•  Efficient Tax (or subsidy) requires policymakers to have a lot of information.

•  Assigning property rights (Coase) is not enough when many agents are involved and transaction costs are high

•  What else can the government do? –  Set emission standards –  Pollution charges –  Create market for the externality through

marketable pollution permits (i.e. combine the best features of standards and charges)

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Standards versus Charges •  We are now deviating from the assumption that the

government knows the socially optimal level of pollution and instead we assume that it tries to decrease pollution to a level that it deems acceptable. This is particularly applicable to cases where a country signs onto a treaty (e.g., the Kyoto Protocol) that commits it to reduce pollution by a set amount. –  That amount may or may not be efficient

•  Standards: The government tells each firm by how much to cut pollution.

•  Charges: The government announces that firms have to pay an environmental fee – a charge – for each unit of pollution. By making polluting more costly the governments hopes to decrease pollution to the target level.

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Two or More Firms and Standards

•  Suppose the government can monitor pollution of each firm and requires each firm to cut pollution by half, to bring down pollution to the acceptable level.

•  Suppose both firms adhere to the government’s standard. Suppose further that sitting at that level of pollution (at the standard), firm A loses $10 in profit if it cuts pollution by yet one more unit, while firm B loses $12 in profit if it reduces pollution by yet one more unit. –  Firm A’s marginal abatement cost=$10 –  Firm B’s marginal abatement cost=$12

•  This is equivalent to saying that firm B would gain $12 in profit if it increased pollution by one more unit, when it’s at the standard.

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Setting Standards is not efficient

•  Both firms could, in theory, be better off if firm A cuts pollution by one more unit than required and firm B increases pollution by one more unit. Both could win if firm B makes a side payment of $11 to firm A to compensate for firm A’s increased pollution reduction costs (each firm gains $1 in this reallocation away from the government standard). Overall, society gains $12 and loses $10 (for a net gain of $2) without changing the total level of pollution.

•  This example suggests that under a standard, there exists a potential Pareto-improvement—in other words, across-the-board cuts are not efficient –  Unless marginal abatement costs for the 2 firms happen

(magically) to be equal at the mandated level of pollution. 39

Two or More Firms and Charges •  In order to bring down pollution to the acceptable

level in a more efficient way, the government can levy charges on the amount of pollution caused by each firm. For example, the government announces that it will charge $10 on every unit of waste dumped into the water.

•  Then each firm will produce and pollute until the marginal benefit (the marginal profit without the charge) is equal to the charge. At the equilibrium, the marginal costs of abatement for both firms will be the same.

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Example

Abatement Firm A’s MAC

Firm B’s MAC

1 3 2 2 6 4 3 10 6 4 15 8 5 21 10 6 28 12

To abate means to cut pollution!

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Example Cont’d •  If the charge is $10, that means firms need to pay

$10 dollars for each unit of pollution they produce, then firm A will abate 3 units and firm B will abate 5 units.

•  With standard for each firm needing to cut back 4 units, the same level of pollution is achieved at a higher cost. –  Work out costs of abatement under each scenario as an

exercise. Do you see that society is better off under the pollution charge system?

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Weaknesses of Standards and Charges

•  The government needs to know a lot to correctly implement charges. It must somehow determine what the acceptable level of pollution is and it must have a good idea by how much pollution will decrease once the charges are in place. If it estimates the costs of abatement incorrectly, firms may decrease pollution by not enough or by too much. On the other hand using charges rather than across-the-board cuts will enhance cost efficiency. –  Charges bring about a given cut in emissions at lowest cost

(but you may end up at an emissions level you weren’t aiming for)

–  Standards guarantee that you hit the emissions target, but you do so at higher cost (due to inefficient allocation of the abatement responsibilities) 43

Marketable Permits

•  Marketable permits combine the advantages of standards and charges: –  The government issues permits in the amount it

will tolerate pollution and hence removes all the uncertainty about whether or not the target level of pollution is reached. This is the advantage over charges.

–  Can collect revenue, while bringing about cost efficient pollution reduction. By having firms bid for permits, the firms will set a price of the permit equal to the marginal benefit of polluting one more unit. Therefore the inefficiency caused by standards does not apply to marketable permits.

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Trading Carbon

•  http://www.cbc.ca/news/background/kyoto/carbon-trading.html

•  Kyoto protocol and Canada: timeline •  http://www.cbc.ca/news/background/

kyoto/timeline.html •  https://en.wikipedia.org/wiki/

Canada_and_the_Kyoto_Protocol 45

Pollution Permits

•  Note that initial distribution of permits (property rights) doesn’t effect efficiency result –  Could sell permits to firms –  Could give permits to firms

•  Could distribute equally across firms •  Could give all to one firm

–  As long as a market for the permits exists, firms will buy the permits so long as the price of the permit is less than their marginal abatement cost

•  Buy permits until P=MAC (marginal abatement cost)

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Govt auction of pollution permits

•  Example: There are three firms in a community that pollute the environment. Each of them is polluting the environment by releasing 7 units of pollution. The government has decided that 12 units of pollution must be abated. The marginal cost of pollution abatement for each firm is given in the table below.

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Unit abated Firm A Firm B Firm C

1 6 3 9

2 8 5 12

3 10 7 15

4 12 10 18

5 14 11 21

6 16 12 24

7 18 16 27

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Govt auction of pollution permits

•  Suppose the government auctions pollution permits using a second price auction. (That is, the highest bidder receives the permit at a price equal to the second highest bid). Without any pollution permits, each firm must abate all of its pollution, that is 7 units.

•  It is a well-established economic result, that in second price auctions, people are best off if they bid equal to their true willingness to pay.

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Govt auction of pollution permits

•  That is, if for example firm A must abate 7 units but now has an option to get a pollution permit, this permit is worth $18 to firm A, because this is exactly how much firm A would save by having to abate one unit less.

•  Sometimes two firms may be the highest bidders. In this case only one firm can receive the permit. To break the tie, give the permit to the firm whose name appears first in the alphabet.

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Permit Firm A’s bid

Firm B’s bid

Firm C’s bid

Winner Price paid

1st 18 16 27 Firm C 18

2nd 18 16 24 Firm C 18

3rd 18 16 21 Firm C 18

4th 18 16 18 Firm A 16

5th 16 16 18 Firm C 16

6th 16 16 15 Firm A 15

7th 14 16 15 Firm B 15

8th 14 12 15 Firm C 14

9th 14 12 12 Firm A 12 51

Explanation of table entries: •  Without a permit, a firm needs to abate 7

units of pollution. •  So how much is it worth to the firm to receive

one permit? •  It’s equal to cost savings of not having to

abate the 7th unit of pollution. –  Thus when the government auctions off the first

permit, firms’ bids equal their MC of abating the 7th unit of pollution.

•  Once firm has purchased one permit, it values another permit equal to the cost savings of not having to abate the 6th unit of pollution, and so on and so forth.

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Auctioning permits is cost efficient

•  Notice that the last permit is bought at a price of 12.

•  Every firm abates pollution until its MC of abating is equal to 12.

•  Buy permits until P=MAC (marginal abatement cost)

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Tradeable Permits--Conclusion

•  This is what “cap and trade” is all about – Likely to be key component of world efforts

to reduce carbon emissions – Cost saving makes it social-welfare

improving over standards –  Increases chance of getting business on

board with emissions reductions (lessens hardship on them per unit of abatement)

– Has Sierra Club support – Obama’s energy plan (currently dead in

Congress) has cap and trade component 54

Externalities and Fairness •  Studies have shown that poor are

disproportionately subject to pollution –  Not surprising, if clean air is a normal good –  Rich may pay real estate premium to live in areas

with clean air and water –  May be concerned that clean air is “fundamental

right”, not commodity •  Interventions can reduce or increase fairness

–  Giving a rich factory owner rights to pollute increases his/her wealth

–  But taxing factory owner will raise price of the product sold--what if poor are primary consumers?

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Externalities and Fairness

•  Interventions that lead to reductions in output (in case of negative externalities) may lead to workers being laid off –  Difficult to assess the distributional impacts of

these attempts at achieving efficiency –  Poor spend a large fraction of income on

transportation; so gas tax or carbon tax is likely to hurt poor more than rich

–  This is not to say it shouldn’t be done. Other redistributive measures could be combined with correction of the externality to neutralize distributional effects of correction

•  BC does this with Carbon Tax