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
wBx
Person B
The endowment point is
not Pareto efficient.
Allowing trade permits
a Pareto improvement
y
wBy
Contract curve
Endowment
wAy
Person A
wAx
x
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
B’s money
s
Smoke
Person A
A’s money
m
Person B
Rights and endowments
B’s money
Person B
s
If B has the right to a
smoke-free environment,
endowment is at
Smoke
Person A
m
A’s money
$100
Smokers’ rights
B’s money
Person B
s
If A has the right to smoke
as much as he wants,
endowment is at
Smoke
Person A
m
A’s money
$100
Neither endowment is necessarily
Pareto efficient
Person B
B’s money
s
Smoke
Person A
m
A’s money
$100
Paying to smoke
B’s money
Person B
s
Allow trade, or
make A pay B per
unit of smoke
Contract curve
Smoke
Person A
m
A’s money
$100
Paying for clean air
B’s money
s
Contract curve
Smoke
Person A
Allow trade, or
make B pay A per
unit of smoke
reduction
m
A’s money
$100
Person B
A and B care about who gets the
property rights!
B’s money
s
Pareto set
Smoke
Person A
m
A’s money
$100
Person B
Quasi-linear preferences
B’s money
s
s*
Smoke
Person A
Pareto set
m
A’s money
$100
Person B
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?
Agent A
Agent B
w(t)
v(s)
Slope = marginal
utility of less smoky air
Slope = marginal
utility of smoky air
t
s
w’(t)
v’(s)
s
t
Marginal costs and benefits
• Pareto efficiency requires v’(s) = w’(t)
A’s marginal benefit
Looks like a demand
curve
B’s marginal cost
of smoke
Looks like a supply
curve
Pigouvian
tax on smokers
0
s
s* 1-s=t
1
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
Firm A’s marginal
benefit
Firm B’s marginal
benefit
Pigouvian tax
on pollution
0
s
s*
1-s
1
Pollution permits
• If A has all the
permits, it sells 1-s* to
B, at price p*
Firm A’s marginal
benefit
Firm B’s marginal
benefit
• If B has all the
permits, it sells s* to
A, at p*
p*
• Only difference is
which firm earns the
profits from permit
sales
0
s
s*
1-s
1
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