1. 14. Externalities
Varian, Chapter 33

2. 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.

3. Missing markets The endowment point is not Pareto efficient.
Person B
wBx y
The endowment point is
not Pareto efficient.
Allowing trade permits
a Pareto improvement
wBy
Contract curve
Endowment
wAy
Person A x
wAx

4. 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

5. Edgeworth box
Person B
B’s money s
Smoke
Person A m
A’s money

6. Rights and endowments If B has the right to a smoke-free environment,
Person B
B’s money s
If B has the right to a
smoke-free environment,
endowment is at
Smoke
Person A m
A’s money
$100

7. Smokers’ rights If A has the right to smoke as much as he wants,
Person B
B’s money s
If A has the right to smoke
as much as he wants,
endowment is at
Smoke
Person A m
A’s money
$100

8. Neither endowment is necessarily Pareto efficient
Person B
B’s money s
Smoke
Person A m
A’s money
$100

9. Paying to smoke Allow trade, or make A pay B per unit of smoke
Person B
B’s money s
Allow trade, or
make A pay B per
unit of smoke
Contract curve
Smoke
Person A m
A’s money
$100

10. Paying for clean air Allow trade, or make B pay A per unit of smoke
Person B
B’s money s
Contract curve
Allow trade, or
make B pay A per
unit of smoke
reduction
Smoke
Person A m
A’s money
$100

11. A and B care about who gets the property rights!
B’s money
Person B s
Pareto set
Smoke
Person A m
A’s money
$100

12. Quasi-linear preferences
B’s money
Person B s s*
Pareto set
Smoke
Person A m
A’s money
$100

13. 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*)

14. 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)

15. 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?

16. Agent A
Agent B
w(t)
v(s)
Slope = marginal
utility of less smoky air
Slope = marginal
utility of smoky air s t
v’(s)
w’(t) s t

17. 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 1 s s*
1-s=t

18. 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

19. 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?

20. 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 1 s s*
1-s

21. 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
Firm A’s marginal
benefit
Firm B’s marginal
benefit p* 1 s s*
1-s

22. 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