Economics 325: Public Economics
Section A01
University of Victoria
Midterm Examination #1
VERSION 1
Section 1: Multiple Choice (3 points each)
Select the most appropriate answer, and circle the corresponding letter on your exam
paper.
Questions 1-3 refer to the following diagram of a perfectly competitive market. No
externality is present.
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1) What is the change in social welfare (aggregate net benefits) going from the
equilibrium quantity to Q=300?
A) It falls by $2,500
B) It rises by $6,750
C) It falls by $1,250
D) It rises by $1,250
E) None of the above
2) What is the variable cost of producing 100 units?
A) $25
B) $100
C) $2,500
D) $10,000
E) None of the above
3) What is the deadweight loss associated with producing 100 units of the good?
A) $1,250
B) $2,500
C) $5,000
D) $7,500
E) None of the above
Questions 4-8 refer to the diagram below. The MSC curve is given to denote the
presence of an externality in this market.
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4) Which of the following statements about this market is/are true?
I. Equilibrium quantity is 100.
II. Efficient quantity is 50.
III. There is a negative externality in this market.
A) I and II only
B) I only
C) III only
D) I, II, and III
E) None of the statements is true.
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5) At equilibrium, total external benefit in this market is
A) $0
B) $2,500
C) $3,375
D) $5,000
E) None of the above
6) What is the maximum gain in social welfare that can be achieved (relative to
equilibrium) with a policy intervention?
A) $0
B) $1,250
C) $3,375
D) $4,375
E) None of the above
7) Which of the following policies would bring about the efficient quantity?
I. A tax of $50 per unit.
II. A subsidy of $50 per unit.
III. A quota at Q=100.
A) I only
B) II only
C) I and III only
D) II and III only
E) None of the above
8) What price will consumers pay for this good under the efficiency-inducing policy?
A) $25
B) $50
C) $75
D) $100
E) None of the above
END SECTION 1.
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Answer each question as clearly and concisely as possible on the exam paper. Use of
carefully labeled diagrams, where appropriate, is strongly encouraged.
Section 2: True, False, or Uncertain (5 points each).
Respond to each of the following statements by labeling the statement “true,” “false,” or
“uncertain.” Then justify your claim. Answers that do not provide justification will
receive zero points.
1) (5 points)
In light of the Coase Theorem, government intervention is probably not needed to solve
major externalities and public goods problems.
False. The Coase Theorem tells us that if we assign property rights to an externality (e.g.
allow a polluter to dump in a river; or allow a fisherperson to have rights to a clean
river) AND if there are zero transactions costs (i.e. costs of negotiating) and zero
monitoring costs (i.e. everyone can tell who is contributing to the externality and how
much) then government intervention (taxes, subsidies, command and control, etc.) is not
required to solve the problem.
Those assumptions are likely to fail in cases of major externalities and public goods
problems. It would be great if everyone paid me for my contributions to a public good,
according to their marginal willingness to pay. But even if I had the right to demand
those payments from people, it would be incredibly costly to collect from everyone who
owes me. And if polluters are going to pay me for the right to pollute the air I breathe, I
have to be able to figure out how much each polluter has contributed, in order to bill
them for the damage they’ve caused me. Policy is going to be a better approach to
solving problems like these examples. While Coase may be sensibly applied to
neighbours sorting out issues over loud music, keeping trees trimmed, weeds controlled,
etc.
2) (5 points)
In equilibrium, with no government intervention, contributions to public goods will be
zero.
False. In general, we can expect some people to make some contributions to public
goods (so long as MPB>MPC) simply because it’s in their self interest. The problem is
they’re unlikely to contribute as much as would be socially optimal for them to
contribute.
Some argue that people contribute to public goods beyond their own self interest—that
they exhibit altruism. So people may give to charities that preserve the environment or
help the poor because they get increased happiness from seeing other people become
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better off. This is another reason (beyond self-interest) that people will contribute to a
public good.
END SECTION 2
Section 3: Short Answers
1) (14 points total)
Consider the market for packs of cigarettes. Assume that the market is otherwise
competitive, but that a negative consumption externality (second-hand smoke; and the
fact that other taxpayers pay for medical care for smokers) is present. Demand and supply
for packs of cigarettes are given in the diagram below.
Diagram for Question 1 (Market for Cigarettes)
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Unless otherwise stated, provide a numeric answer to the questions below.
a) 3 points
What is social welfare (aggregate net benefits) in equilibrium? You must show your
work to receive credit.
Equilibrium occurs where MPC=MPB, at Q=200.
SW=TSB-TSC
TSB at Q=200 is the area of the trapezoid under the MSB curve between Q=0 and
Q=200. This has an average height of 5 and a base of 200, or an overall area of 1000.
TSC at Q=200 is the area of the trapezoid under the MSC curve between Q=0 and
Q=200. This has an average height of 5 and a base of 200, or an overall area of 1000.
So, SW=TSB-TSC=1000-1000=0.
You can also use the formula SW=CS+PS-TEC
But isn’t the first way of doing things much simpler? Always go with the easy approach,
if it’s appropriate. And here you’ve got the MSB and MSC curves so TSB and TSC are
easy to find.
Note that if you said SW=CS+PS, you’re missing the point of externalities! Go back and
think carefully about why that statement is wrong in this context.
b) 3 points
Clearly illustrate and label in the diagram the area that best represents deadweight loss in
equilibrium in this market. You don’t need to provide a number.
I asked you to do this in the diagram because there are two triangles with the same area,
one of which captures DWL. I’ve shaded that triangle above.
If you want to remember this formulaically, it’s the area bounded by Qeff, Qeq, MSC, and
MSB.
A better way to think of it is that if we were to move from Q=200 to Q=100, we’d gain a
cost reduction equal to the trapezoid under MSC between Q=100 and Q=200; and we’d
forgo the benefits given by the trapezoid under MSB between Q=100 and Q=200. Taking
the difference of those two trapezoids yields the shaded area above—the DWL. This is
the social welfare we forego by being someplace (in this case, the equilibrium) other than
the efficient quantity.
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If you like it stated a slightly different way, the increased cost to society of going from
Q=100 to Q=200 is the trapezoid under MSC. The increased benefit to society is the
(smaller) trapezoid under MSB. Therefore SW falls by the difference in these trapezoids
when we move from the efficient quantity to the equilibrium. This difference is the DWL
associated with being at the equilibrium.
Try to get the intuition for this.
c) 2 points
What would be the price producers would receive, if the optimal tax (the tax that
maximizes social welfare) were imposed?
The purpose of a tax to address a negative externality is to “internalize” the externality—
that is to make the agent who causes the externality “feel the pain” of the externality
through the tax. This way, even though they still don’t care about the externality, they do
care about the tax. So if we perfectly match the pain of the tax (to the agent causing the
externality) to the pain of the externality, the agent causing the externality will act “as if”
they care about the externality. The tax doesn’t have to match the externality at every Q.
Just at Qeff, because that’s where we want to end up. So the optimal tax (i.e. the tax that
maximizes social welfare by moving the market to Qeff) is the tax that is equal to the
marginal external cost (the pain caused by the externality) at Qeff. This is $5 in this case,
as you can see in the diagram above.
If we impose a per unit tax of $5, this will push the market to a new equilibrium at
Q=100. I’m assuming the tax is placed on producers, so I illustrate this above by putting
in a taxed MPC curve for producers. This is just MPC+t* or MPC+5. It’s just a vertical
shift upwards by the amount of the tax.
Here the price paid by consumers is $10. Producers get this payment per unit from
consumers but then hand $5 over to the government in the tax they pay. Therefore they
are left with only $5 per unit in their pocket. So $5 is the price received by producers.
This is labeled Ps above.
d) 3 points
What would be consumer surplus with the optimal tax in place? You must show your
work to receive credit (for partial credit you can shade and clearly label the relevant area
in the diagram above).
Consumer surplus is the total private benefit consumers get from Q=100 minus their total
expenditure (which includes tax payments). This is the small triangle labeled above.
This has an area of $2.50*100/2=$125.
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e) 3 points
What would be government revenue with the optimal tax in place? You must show your
work to receive credit (for partial credit you can shade and clearly label the relevant area
in the diagram above).
Government revenue is the yellow area shaded above. This is just Q*t. Or
100*$5=$500. Make sure you’re clear on the intuition for why GR=Q*t.
2. (12 points total)
Question 2 (public goods) refers to the diagram below:
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There are only three consumers in this market for a public good. They have individual
demand curves D1, D2, and D3, respectively.
a) 4 points
Carefully draw the marginal social benefit curve for the public good on the diagram
above.
(see diagram above)
Remember, you get the MSB curve by vertically aggregating the individual MPB curves
(demand curves). One way to do this is to, at each vertical gridline, add up the MPB for
each person, and plot the sum as a point on the MSB curve. Try this if you got it wrong.
You have to get your hands dirty practicing this stuff to get used to it.
b) 3 points
If the marginal cost of providing the public good is $45 per unit, what is the efficient
quantity of the good? You must clearly show your work to receive credit.
I’ve illustrated the marginal cost curve on the diagram above. Note that if the marginal
cost is a constant, this line is horizontal. Some people wanted to draw a MC curve with a
slope of 45. That’s incorrect.
To find the efficient quantity, we set MSC=MSB. MSC=45, so that part’s easy. We need
an equation for MSB representing the segment of the MSB curve that the MSC curve
intersects. Obviously, a picture is very useful here.
Note that MSC crosses MSB in the middle segment of MSB. In order to find an equation
for that curve, I project the line back to the y-axis (see the dotted line). By inspection we
see that the equation for this line is MSB=125-(1/2)Q. How did I get this? Remember
your slope-intercept formula from high school algebra? y=b+mx, where b=y-intercept
and m=slope? Well y in this case is MSB; x in this case is Q; b is 125; and m is -1/2.
So, setting MSC=MSB, we get 45=125-(1/2)Q. Rearranging gives us (1/2)Q=80, or
Q=160. That’s the efficient quantity.
c) 5 points
Suppose that there were no contributions to the public good. Calculate the deadweight
loss in that situation. You must clearly show your work to receive credit (for partial
credit you can shade in the area representing DWL in the diagram above).
If there are no contributions, then the quantity of public goods is zero. I’ve redrawn the
diagram shading in DWL below. It’s the area between MSB and MSC between Q=0 and
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the efficient quantity (Q=160). These are all positive net benefits that could be had, if
public goods were provided at the efficient level. To calculate the area, you should find
the area of the trapezoid between Q=0 and Q=100, and the area of the triangle between
Q=100 and Q=160.
Trapezoid: 6750
Triangle: 900
Total DWL: $7650
END SECTION 3.
END OF EXAM.
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