FE431: PUBLIC FINANCE
Fall 2012
Professor Schmitt
Homework 2 – due 18 September
1. (30 points) The supply of flu shots is described by the following equation: QS = 4P,
where QS is quantity supplied per day and P is the price per shot. The demand is
described by QD = 500 – P, where QD is shot demanded per day. Because of the external
benefits to society associated with flu shots, there is a marginal external benefit of $25
are associated with each flu shot.
a) (10 points) Assuming that flu shots are sold in a competitive market, show this situation
graphically. Be sure to properly label your graph and indicate if this market is efficient or
inefficient. If it is inefficient, clearly show the deadweight loss.
P
525
MSC = MPC + 0(MEC)
500
A
DWL
Pproducer
=105B
PC=100
Pconsumer
C
D
= 80 E
MSB = MPB + MEB
F MPB
QC = 400 Qefficient = 420
b) (5 points) Assuming that flu shots are sold in a perfectly competitive market, what is the
market price per day? How many flu shots will be produced per day at that price?
QS = QD = 500 – 1P = 4P
 500 = 5 P
or P = 500/5 = $100 per day
Plug P into either QS or QD 
500
– 5*100 = 4*100 = 400 = QC
c) (5 points) What is the efficient annual output of flu shots? How can this level of output
be achieved?
Taking the positive externality into account –
MSB = MPB + MEB but in order to calculate this, you cannot merely add to the MEB,
you need to rearrange your QD equation
 QD = 500 – P now becomes P = 500 – QD
Adding the MEB to this yields, P = 500 – QD + 25 which can be rearranged to give you
QD = 525 – P
Re-equate this to MSC  525 – P = 4P  525 = 5P
Or P = 525/5 = $105 a day (although this is not the “real price” this price would give the
efficient quantity, but note that consumers would not get to the efficient output if prices
were $105).
This yields an efficient output of Qefficient = 420
QS = 4*P = 4*105, or QD = 525 – P = 525 – 105 = 420
Again, consumers wouldn’t purchase 420 units at $105 (need to look at MPB), at $105,
they’d only buy MPB = QD = 500 – 105 = 395, so the government may need to subsidize
– they’d set subsidy = MEB = $25.
It is reasonable to assume that Coase Theorem would not hold as the bargainers would
have difficulty identifying themselves, there are a large number of bargainers,
information may not be known, and zero transactions costs probably isn’t a good
assumption.
d) (10 points) What was the inefficiency associated with the inefficient level of output?
(Recall that the area of a triangle is ½ b*h.) Shade it on your graph.
The area above ACD – to calculate, we need to figure out what the price at A is: To do
that, you need to see what is the price at the MSB = 525 – P = 400, or P = 125. Now, just
use the ½ bh:
½ b*h = ½ (420 – 400)*(125-100) = ½ * 20 * 25 = 250,
Therefore the total DWL is 250 the area ACD in the graph.
2. (10 points) Warrenia has two regions. In Oliviland, the marginal benefit associated with
pollution cleanup is MB = 300 – 10Q, while in Linneland, the marginal benefit associated
with pollution cleanup is MB = 200 – 4Q. Suppose that the marginal cost of cleanup is
constant at $12 per unit. What is the optimal level of pollution cleanup in each of the two
regions?
The optimal level of cleanup will occur when the marginal benefit just equals the
marginal cost. In Oliviland, the marginal benefit is 300 – 10Q; marginal cost is 12.
Therefore, the equation to solve for Oliviland is 300 – 10Q = 12, or 288 = 10Q. The
optimal level in Oliviland is 4 equal to 28.8. For Linneland, the marginal benefit is 200 –
4Q. Setting the benefit equal to 12 yields 200 – 4Q = 12, or 188 = 4Q. The optimal level
in Linneland is equal to 47.
3. (10 points) In which way could smoking exert a positive externality on others?
The reduction in expected lifetimes can deliver a positive externality. If smokers tend to
die soon after their retirement, they will collect less in Social Security payments, leaving
more money for nonsmokers. In addition, if smokers pay into group retirement plans
that do not differentiate smoking behavior, then their reduced time of withdrawal from
the plans will subsidize the longer-lived nonsmokers.
4. (10 points) Caffeine is a highly addictive drug found in coffee, tea, and some sodas.
Unlike cigarettes, however, there have been very few calls to tax it, to regulate its
consumption, or limit its use in public places. Why the difference? Can you think of any
economic arguments for regulating (or taxing) it’s use?
Unlike cigarettes, caffeine does not cause any obvious externalities (e.g., secondhand
smoke). If we believe Becker and Murphy’s rational addiction model, then addictiveness
does not provide a motivation for regulating a good—only externalities do. On the other
hand, if people have self-control problems, then “internalities” could potentially provide
a motivation for taxing or otherwise regulating caffeine. This is particularly true for
children, who tend to be short-sighted and may not fully appreciate the long-term
consequences of caffeine addiction. This might be a reason to regulate sales of sodas
containing caffeine in schools, for example.
5. (40 points) Use the following graph for the production of good X:
P
MSC
MC
DWL
30= MD
120
60 100
Quantity
a) (10 points) Using the graph above, assume that the production of good X generates
pollution. Assume that the environmental damage is $30 per unit of good X and that
the socially optimal output of X is 60. Add these numbers to the graph above.
b) (20 points) Assume there is no policy to correct for the environmental damage: For
the 100th unit of good X; what is the MB to consumer? The marginal private cost?
The marginal social cost? The marginal net loss to society? The net loss to society
(deadweight loss) – shade this area on the given graph?
MB to consumer = $120
MPC = $120
MSC = $150
MD (marginal net loss) = $30
Net loss = $600 [(1/2)($30)(40)=$600]
c) (10 points) What tax would achieve the social optimum? And what (and in which
direction) are the curves in the given graph changed with a tax? What happens to
market price and quantity?
T = MD = $30
S shifts up, Price of X increases, quantity of X decreases.