14. Externalities

Varian, Chapter 33

Types of externalities

• Consumption externalities– Consumption of a good by agent A has a

direct impact on agent B’s utility– E.g., smoking, loud music, tidy garden, etc.

• Production externalities– Actions by agent A have a direct impact on

agent B’s production possibilities– E.g., bee-keeper and apple orchard, polluting

firm and fisherman, etc.

Missing markets

Person A x

y

Person BwBx

wAy

Endowment

wBy

wAx

Contract curve

The endowment point isnot Pareto efficient.Allowing trade permitsa Pareto improvement

Room-mates

• 2 agents A and B

• There are two “goods”:– Stuff – i.e., money: mA and mB : Endowments = $100

– Smoke – concentration: 0 ≤ s ≤ 1

• A is a smoker: uA(mA,s)

• B is a non-smoker: uB(mB,t), where t = 1-s

• Note: s + t = 1

Edgeworth box

Person A m

s

Person BB’s money

Smoke

A’s money

Rights and endowments

Person A m

s

Person BB’s money

Smoke

A’s money$100

If B has the right to asmoke-free environment,endowment is at

Smokers’ rights

Person A m

s

Person BB’s money

Smoke

A’s money$100

If A has the right to smokeas much as he wants,endowment is at

Neither endowment is necessarily Pareto efficient

Person A m

s

Person BB’s money

Smoke

A’s money$100

Paying to smoke

Person A m

s

Person BB’s money

Smoke

A’s money$100

Contract curve

Allow trade, ormake A pay B perunit of smoke

Paying for clean air

Person A m

s

Person BB’s money

Smoke

A’s money$100

Contract curve

Allow trade, ormake B pay A perunit of smokereduction

A and B care about who gets the property rights!

Person A m

s

Person BB’s money

Smoke

A’s money$100

Pareto set

Quasi-linear preferences

Person A m

s

Person BB’s money

Smoke

A’s money$100

Pareto sets*

The Coase Theorem

• Coase Theorem: If – property rights are well-defined,– bargaining over the externality is possible

• with sufficiently low transaction costs

– the outcome will be efficient• When preferences are quasi-linear, the

allocation of property rights has no impact on the equilibrium quantity of smoke (s*)

Using demand curves

• Let’s assume quasi-linear preferences• A’s utility: uA(m,s) = mA + v(s)

• A’s marginal benefit from smoke is v’(s)

• B’s utility: uB(mB,t) = mB + w(t)

• B’s marginal benefit of less smoke is w’(t)

Example: smoking

• A’s utility: uA(m,s) = mA + ln(s)• mA = 50

• B’s utility: uB(mB,t) = mB + 2ln(t)• mB = 150

• What are equilibrium s, t, mA, and mB if A has the right to smoke as much as he wants?

• What if B has the right to clean air?

s t

Slope = marginalutility of smoky air

Slope = marginalutility of less smoky air

w(t)

v(s)

Agent A Agent B

v’(s) w’(t)

s t

Marginal costs and benefits

• Pareto efficiency requires v’(s) = w’(t)

s0 1

A’s marginal benefitLooks like a demandcurve

B’s marginal costof smokeLooks like a supplycurve

1-s=ts*

Pigouviantax on smokers

Pigouvian tax

• Definition: A tax on activities with negative externalities

• Double benefit– Reduce harm from negative externalities– Fund useful government spending

• Especially beneficial when Coase theorem does not apply

Example: smoking

• A’s utility: uA(m,s) = mA + ln(s)• mA = 50

• B’s utility: uB(mB,t) = mB + 2ln(t)• mB = 150

• ‘what sort of government tax on smoking x would lead to an efficient outcome?

• What are mA and mB in this outcome?

Allocating pollution amongst firms• Suppose one unit of pollution is to be allocated

between two firms

s0 1

Firm A’s marginalbenefit Firm B’s marginal

benefit

1-ss*

Pigouvian taxon pollution

Pollution permits

• If A has all the permits, it sells 1-s* to B, at price p*

• If B has all the permits, it sells s* to A, at p*

• Only difference is which firm earns the profits from permit sales

s0 1

Firm A’s marginalbenefit

Firm B’s marginalbenefit

1-ss*

p*

Why don’t people cooperate?

• Two firms could merge so as to internalize the costs they impose on each other

• Room-mates can agree on smoking limits, or switch partners

• But there may be transactions costs that limit agents’ ability to trade– E.g., if the market is one-sided – one polluter

and many pollutees