Econ 1, Fall 2010
Problem Set 7 Solutions
University of California, Berkeley
Page 1 of 8
Problem Set #7 Solutions
1. Externalities: Suppose that we have a demand for energy:
Q
D
= 2,000,000 – 25
P
, where
Q
D
is the total
amount of energy consumption in gigawatt hours (GW
∙
h) and
P
is the price of power per gigawatt hour.
Suppose, further, that we have a competitive industry of power plants that can produce up to 2,000,000
GW
∙
h of energy at a constant marginal cost price of $40,000 per gigawatt hour.
Suppose, further, that each
GW
∙
h of energy produced imposes $1 of acid rain damage on fish, buildings, and forests.
a. What is the equilibrium price and quantity in the freemarket equilibrium?
Since this is a competitive market, the supply function is given by
P
=
MC
= 40,000 for all
quantities such that
Q
S
≤
2,000,000.
Therefore, the freemarket equilibrium occurs where
P
=
40,000, and
Q
D
= 2,000,000 – 25(40,000) = 1,000,000 GW
∙
h.
b.
What is the best pollutioncontrol tax to impose on the power plant?
Why?
In general, the optimal tax is equal to the marginal damage cost at every quantity level.
This way,
the marginal damage cost will be incorporated in the marginal cost calculations of the decision
maker, and the externality will be effectively internalized.
In this case, the marginal damage cost is a constant $1 per GW
∙
h for all quantity levels, so the
optimal tax is also a constant $1 per GW
∙
h for all quantity levels.
c. What is the equilibrium price and quantity in the optimal tax equilibrium?
Incorporating the optimal tax, the virtual supply curve is
P
= 40,000 + 1 = 40,001, so the
equilibrium price with the tax in place is P = 40,001, and the equilibrium quantity with the tax is
Q
D
= 2,000,000 – 25(40,001) = 999,975 GW
∙
h.
d. What do you think is the best way to use the tax revenue raised by the pollution control tax?
This is a subjective question with many possible answers.
Nevertheless, it seems particularly
appropriate to spend the $999,975 of tax revenue on measures designed to mitigate the resulting
acid rain damage.
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Econ 1, Fall 2010
Problem Set 7 Solutions
University of California, Berkeley
Page 2 of 8
2. Externalities: Reconsider question 1.
Assume that the demand curve, supply curve, and marginal damage
cost curve are the same as in the statement of question 1.
a. Suppose that you are not allowed—for political reasons—to impose a tax, and instead Production
Distribution Coordination (PDC) imposes a limit on how much of power plant capacity can be operated.
What should that limit be?
The socially optimal quantity to produce is found where the marginal benefit to society (given by
the demand function) intersects the marginal social cost—that is, the sum of the marginal cost to
producers plus any marginal damage cost.
The equilibrium quantity with the optimal tax found
in question 1c is the socially optimal quantity of energy to produce.
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 Fall '08
 MarthOlney
 Economics, Externalities, Producer Surplus, Supply And Demand, producer

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