Professor Gregory Clark
ECN 1A, Fall 2012
ECONOMICS 1A: PROBLEM SET 9
The Role of Government
Externalities
1. (a) List three goods or activities with negative externalities.
Fossil fuels, smoking, garbage, loud music, automobiles in general, SUVs, poorly
maintained properties, dogs, tall buildings
(b) List three goods or activities with positive externalities.
Investments in knowledge, pleasant gardens, bee keeping, immunization of children, cities,
painting your house
2. Suppose the market for gasoline in California is competitive. Demand for gasoline per day is
given by Qd = 20 - 2P, where P is the price in $ per gallon, and demand is measured in millions
of gallons per day. The supply of gasoline is given by Qs = -4 + 10P.
(a) Work out the free market quantity and price.
Set Qs = Qd, and solve for P.
20-2P = -4+10P
24=12P
P*=2
Find Q by plugging P into demand (or supply curve)
Q*=20-2(2)
Q*=16
(b) Suppose that each gallon of gasoline consumed imposes external costs from air pollution,
global warming, environmental damage, and noise of $2. Calculate the efficient quantity
consumed, and the efficient free market price.
Since consumption of gasoline imposes external costs in the form of pollution,
these additional costs should be included in marginal cost:
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New Qs = -4 +10 (P - external cost) = -4 + 10(P - 2)
New Equilibrium: -4 + 10 (P - 2) = 20 - 2P
-4 + 10P – 20 = 20-2P
P* = 44/12 = 11/3
Plug P* into demand curve to get: Q* = 20-2( 11/3) = 38/3
(c) What is total social surplus at the free market price, and at the efficient level of production?
Social Surplus at free market price:
CS = (10 – 2) x (16) x ½ = 128/2 = 64
PS = (2 - .4) x (16) x ½ = 25.6/2 = 12.8
Total Social Surplus = CS+ PS – external costs
= 64 + 12.8 – (16 x 2) = 76.8 – 32 = 44.8
Social Surplus at efficient level of production
CS = (10-3.66) x (12.66) x ½ = 40.13
PS = (3.66- 2.4) x (12.66) x ½ = 7.97
TS = 40.13 + 7.97 = 48.1
(d) Show that a tax of $2 on gasoline consumption will lead to the efficient outcome.
If we impose a tax on consumers, then the amount consumers pay for gasoline is
(P + tax) = (P + 2). New Qd = 20-2 (P + 2)
Equilibrium with tax: 20-2(P + 2) = -4 + 10P
20 - 2P – 4 = -4 + 10P
P* = 20/12 = 1.66
Note: since P+2 = 3.66 is how much consumers pay then plug P+2 into Qd:
Q* = 20 – 2(3.66) = 12.66
If you want to use Qs, then note that P is how much suppliers receive (T goes to
government).
Q* = -4 + 10P = -4 + 10 (1.666) = 12.66
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Notice that quantity produced with a $2 tax is exactly the efficient production
level.
(e) Explain why other measures to limit gasoline consumption such as fuel economy
requirements or emission controls will be less efficient than a gasoline tax.
Other measures like limiting gasoline consumption will not be efficient because
agents will not consume gasoline until their marginal benefit = social marginal cost. High
demanders are asked to limit their consumption even though they are able and willing to
pay for gasoline and the associated external costs. Low demanders, who cannot afford to
pay gasoline and the external costs, are using gasoline because no taxes are imposed, so
the prices are kept low.
Public Goods
3. Suppose the demand curve for Davis Public Radio Station KDAV is given per hour by
Q = 1,000 - 100P
Suppose the cost of being on the air per hour is a fixed $2,000.
(a) Show that it is efficient for KDAV to be on the air.
note: MC = 0
Total surplus = CS + PS– total cost = (10 x 1000 x ½) + 0 - 2000 = 3000
The radio station is efficient because by being on the air, the radio station maximizes
total surplus = $3000
(b) KDAV funds itself by periodic fund raising drives where annoying appeals to people’s
public spiritedness replace the regular programming. Explain why this is inefficient.
It is inefficient because it shifts the demand curve down, hence generating a decrease
in total surplus.
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(c) The radio tries to promote giving by noting that if every listener were to refuse to donate,
then there would be no service. What should a self-interested listener do?
Give nothing.
(d) What is an efficient way to fund KDAV?
Subsidy from the general tax revenue.
(e) Under the efficient fund raising scheme how can the value of KDAVs services be estimated?
Listeners’ contributions in theory should be a good measure of the value of the station.
Unfortunately, this does not work in real life, because listeners can free ride. People who
are asked how much they benefit from the radio station would underestimate their benefits,
if they know that they have to contribute this amount. If they know they will not have to
contribute but still want to hear the station they will overestimate their benefits.
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