Exam 1 Review Problems
1.) Consider a section of freeway that is uncongested during off-peak hours, but congested
during rush hour. Suppose the trip to and from work takes 40 min. when the freeway is
uncongested. Also, supposed that taking the side streets to and from work always takes 60 min.
On the freeway, assume congestion effects occur only after the 3rd car. After the 3rd car, each
additional car that enters the freeway adds 5 minutes of travel time to all freeway commuters.
Lastly, assume that all commuters value their time at $12/hour (or, equivalently $.20/min).
a.) Given the open access to the freeway, how many cars will travel on the freeway?
Cars
1
2
3
4
5
6
7
8
9
10
ave. time
40
40
40
45
50
55
60
65
70
75
total time
40
80
120
180
250
330
420
520
630
750
marginal time
40
40
40
60
70
80
90
100
110
120
Cars will enter to the point that average time on the freeway is equal to the trip time on the side
streets. As a result, 7 cars will enter when there is open access to the freeway.
b.) Suppose the freeway is now privately owned. What toll would be charged by the owner and
how many cars would now travel on the freeway?
The owner would charge a toll such that cars would enter the freeway to the point where
marginal time is equal to the trip time on the side streets. As a result, 4 cars will travel on the
freeway when it is privately owned. And, the owner will charge a toll of $3.
c.) Which situation is efficient (i.e. open access freeway vs. privately owned freeway)? WHY?
The open access freeway is inefficient because cars 5, 6, and 7 could be allocated to different
routes (i.e. the side streets) to decrease total commute time of all commuters. The privately
owned freeway is efficient because cars 1 through 4 could not be reallocated in any other manner
to decrease the total trip time of all commuters.
2.) Assume a city of 1,000,000 people, 60% of whom are willing to pay $1 maximum (each) to
clean up pollution. The rest of the population is better off and is willing to pay $100 each to
clean up pollution. Pollution clean-up costs $2,000,000. It has been proposed that each person
be taxed equally to pay for the pollution clean-up. Will that pass a majority-rule vote? Is it
desirable from the point of view of the Pareto criterion? Is it desirable from the point of view of
the compensation principle? Explain each of your answers briefly.
“Taxing each person equally” means a $2 tax to all residents. A vote on this proposition would
fail to gain a majority, since 60% of the population is willing to pay only $1 to reduce pollution,
and would therefore be expected to vote against it. By the same logic, this proposition as it
stands is not a Pareto improvement: the 60% would be made worse off by paying $2 for
pollution control when their willingness-to-pay is $1.
The proposal is desirable, however, using the compensation principle. The 40% willing to pay
$100 could compensate the 60% sufficiently to gain their support. $1 to each of these 600,000
residents requires $600,000. The other 400,000 residents have a surplus of (100-2)*400,000 =
$39,200,000. That is, we should say they could easily compensate the 60%. The compensation
principle states that this proposition is desirable because this possibility exists, even if the
compensation doesn’t actually take place.
3.) The initial cost of constructing a temporary dam that is expected to last for 5 years is $100
million. The annual net benefits will depend on the amount of rainfall: $18 million in a “dry”
year, $29 million in a “wet” year, and $52 million in a “flood” year. Meteorological records
indicate that over the last 100 years there have been 86 “dry” years, 12 “wet” years, and 2
“flood” years. Assume the annual benefits, measured in real dollars, begin to accrue at the end
of the first year. Using the meteorological records as a basis for prediction, what are the net
benefits of the dam if the real discount rate is 5 percent?
The first step is to calculate the expected value of the annual net benefits:
(.86)($18 million) + (.12)($29 million) + (0.02)($52 million) = $20 million
The second step is to find the present value of the stream of annual net benefits:
($20 million)/1.05 + … + ($20 million)/1.055 ≈ $87 million
Lastly, subtract the cost of construction from the present value of the annual expected benefit
stream to obtain the overall present value of expected net benefits:
$87 million - $100 million = -$13 million.
Thus, the dam is not built.
4.) Suppose we have an efficiently operating market for good X. Also, suppose the government
adds a sufficiently large quantity of good X to the market such that the price of good X decreases
(as shown in the graph below).
Use the graph below to answer the following:
a.) (3 points) The gain in consumer surplus is given by what area on the graph? P0abP1
b.) (2 points) Which supply curve do private sector suppliers operate on, S or S’? S
c.) (3 points) The loss in producer surplus is given by what area on the graph? P0acP1
d.) (2 points) What area on the graph represents the net surplus among producers and
consumers? Is this net surplus positive or negative? abc, and this amount is positive
e.) (3 points) Government surplus is given by what area on the graph? Q2cbQ1
-Government sells (Q2 – Q1) units at price of P1
f.) (2 points) The overall gain in social surplus is given by what area on the graph? Q2cabQ1
Q. What have we ignored? Costs to government of supplying additional units.
Px
S
f
S’
a
P0
b
c
P1
e
D
d
Qx
Q2
Q0
Q1
5.)
Consider the following extended form game (□: decision node. ○: random selection of state of nature)
Cflood|dam
P1
1st
year
Cflood|dam
P2
2nd
year
Build
dam
1-P2
1-P1
0
0
1-P2
Cdam
0
P2
Do not
build dam
Cdam
1-P1
Cflood|dam
0
1-P2
0
P1
P2
Cflood|no dam
Cflood|no dam
This is a two period game where a town faces the decision of whether or not to build a dam to protect against flooding. The dam will
cost Cdam. The town faces this decision over a two year span. If the town builds the dam in the first year, then it does not face the
choice of building the dam in the second year (because it is already built). If the town does not build the dam in the first year, then it
has the option of building the dam in the second year. Regardless of whether the dam is built in the first year, the town faces the
chance that a flood occurs (with probability P1). If the town builds the dam and the flood occurs, then the town incurs costs of
Cflood|dam. If the town does not build the dam and the flood occurs, then the town incurs costs of Cflood|no dam. The probability of the
flood occurring in the second year is P2.
a.) Suppose the dam is not built in the first year (i.e. consider the bottom half of the decision tree). What is required for building the
dam in the second year to be the dominant strategy?
Cdam + P2Cflood|dam < P2Cflood|no dam
b.) Suppose your answer to part a.) holds (i.e. if the dam is not built in the first year, then the dominant strategy is to build the dam in
the second year). What are the expected costs of building the dam? What are the expected costs of not building the dam? (These will
be present value estimates because the expected costs cover two time periods.)
E[costs of building] = Cdam + P1Cflood|dam + [{P2Cflood|dam}/(1+d)](1-P1)
E[costs of not building] = P1Cflood|no dam + [{Cdam + P2Cflood|dam}/(1+d)](1-P1)
where d is a discount rate
c.) Suppose that Cflood|no dam = 2*Cflood|dam. What is required for the town to build the dam in the first year?
If [d/(1+d)]*Cdam – P1Cflood|dam > 0, then the town will build the dam in the first year.
6.) Assume a country imposes an import fee on the crude oil it imports. Assume that prior to the
imposition of the import fee, the country annually consumed 900 million short tons of coal, all
domestically mined, at a price of $66 per short ton. How would the CBA of the import fee
change if, after imposition of the import fee, the following circumstances are assumed to result
from energy consumers switching from crude oil to coal?
a. Annual consumption of coal rises by 40 million short tons, but the price of coal
remains unchanged.
As long as the secondary market for coal is undistorted and its price does not change, the
increased consumption of coal is irrelevant to estimation of changes in social surplus in the
primary (crude oil) market.
b. Annual consumption of coal rises by 40 million short tons and the price of coal rises
to $69 per short ton. In answering this question, assume that the prices of other
goods, including coal, were not held constant in estimating the demand schedule for
crude oil.
Since it was assumed that the price of other goods, including coal, were not held constant in
estimating the primary market (crude oil) demand schedule, the crude oil demand curve can be
viewed as an equilibrium demand curve. Consequently, there is no need to consider changes in
the secondary market for coal.
c. The market price of coal underestimates its marginal social cost by $15 per short ton
because the coal mined in the country has a high sulphur content that produces smog
when burned. In answering this question, assume that, as in question 2.a, the annual
consumption of coal rises by 40 million short tons, but the price of coal remains
unchanged.
If the market for coal is distorted with an externality, then a relevant social surplus change occurs
even if price does not change. In this case, the social surplus loss in this secondary market would
be (40 million short tons)($15 externality per short ton) = $0.60 billion/per year.
Note that all of the analyses in the answers to question 3 in Chapter 4 and to this question
assume that there are no externalities in the primary (crude oil) market. If there were an
externality in this market, then the import fee would generate additional benefits because total
crude oil consumption falls. Of course, the switch to coal might very well involve an even larger
social surplus loss due to environmental externalities.