Midterm
ECNS 432
February 28, 2013
________________________Name
You may use a calculator, but nothing else on this exam!
1.) (15 points total) On a certain section of freeway, 3 cars can travel without impeding each
other’s speed. They all travel to and from work, and when the freeway is uncongested, the trip
takes 30 minutes. Travel on the side streets takes 1 hour. Each succeeding car beyond car #3
slows everyone up by an additional 4 minutes. All commuters earn $6.00 per hour, and value
their time accordingly.
a.) (6 points) How many cars will use the freeway if access is unrestricted? Explain why this is
an inefficient use of the road.
10 cars will take the free if access is unrestricted. This is inefficient because cars 6 through 10
could be reallocated to the side streets to reduce the total travel time for all commuters.
b.) (6 points) Recently, some brave politicians have advocated “user-fees”, i.e. tolls, on
freeways. Explain why such a system could lead to efficient use.
With open access, there is no mechanism for restricting access and, thus, rents are driven to zero.
Private ownership coupled with a “user fee” will effectively restrict access to those that are not
WTP the amount to take the freeway. This has the potential to lead to the efficient number of
cars on the freeway.
c.) (3 points) Explain why a private owner would charge a toll that produced efficient use of the
freeway. What is that toll in this case?
When the road is privately owned, the owner “owns” not only the rents generated, but
also all the damages inflicted on other drivers as congestion increases. The owner will charge a
toll of $2.20 to induce the efficient 5 cars to use the freeway.
2.) (15 points) Suppose we have a three person neighborhood consisting of a gardener named Arnold
and his neighbors Sylvester and Jean Claude. Arnold plants flowers in his garden every year because he
gets benefits from being able to enjoy a nice looking yard. In addition, Sylvester also gets benefits from
being able to enjoy the flowers that Arnold plants. However, Jean Claude has bad allergies and the pollen
from the flowers make his allergies worse. Assume that Arnold gets $100 of benefits from each batch of
flowers that he plants. Also, assume that Sylvester gets $50 in benefits from each batch of flowers that
Arnold plants. Lastly, assume that Jean Claude’s allergy medication costs increase $20 for each batch of
flowers that are planted. In addition, suppose that Arnold faces the following marginal cost schedule for
planting flowers:
Q(# of batches of flowers)
1
2
3
4
5
6
7
8
Arnold’s MC
25
40
65
80
100
125
150
180
a.) (7 points) Due to Arnold’s extremely thick accent he cannot communicate with his neighbors
(i.e. transaction costs to communication and negotiation are prohibitively high). How many
batches of flowers will Arnold plant? Is this outcome socially efficient? Why or why not?
Arnold will plant to the point where his pvt. MC = pvt. MB. He plants 5 batches of flowers.
This is not socially efficient b/c this is not taking into consideration benefits/costs to the other guys.
b.) (8 points) Now assume Sylvester and Jean Claude each have an interpreter so they can
understand Arnold. Assume the interpreters are free of charge so communicating with each other
is now costless (i.e. transaction costs are zero). How many batches of flowers will Arnold plant?
Is this outcome efficient?
Now, Arnold will plant to the point where soc.MC = soc.MB. Thus he plants 6 batches. This is efficient
because all mutually beneficial gains from trade have been exhausted.
3.) (10 points total) Suppose MSU is trying to decide how to use a piece of land. One option is
to put up an outdoor rock climbing wall with an expected life of 3 years. Another is to install an
outdoor swimming pool with an expected life of 6 years. The climbing wall would cost
$120,000 to construct and would yield net benefits of $46,000 at the end of each of the 3 years.
The swimming pool would cost $500,000 and would yield net benefits of $100,000 at the end of
each of the 6 years. Each project is assumed to have zero salvage value at the end of its life.
Using a real discount rate of 5 percent, which project offers larger net benefits? (HINT: Notice
that the proposed project lengths are not the same.)
As only one of these projects can be built on the site, they are mutually exclusive. The
comparison is complicated because the swimming pool has an expected life two times longer
than the rock climbing wall.
Consider first the NPV of each project separately:
NPV(one climbing wall project)
3
  $120,000  
i 1
46,000
 $5,269
(1  0.05) i
NPV(one swimming pool project)
6
  $500,000  
i 1
100,000
 $7,569
(1  0.05) i
If we choose on the basis of this comparison, then the swimming pool has a larger present
value of net benefits. However, this is not appropriate as the projects are of different lengths.
One possible correct approach is the following:
One could choose between one swimming pool and two successive climbing wall projects so that
the site is used in each case for the same length of time.
NPV(two successive climbing wall projects)
= $5,269 + $5,269/(1+.05)3
= $9,821
Thus, two successive climbing wall projects offer a higher present value of net benefits
than the swimming pool project. One should build the climbing wall.
4.) (10 points total) Imagine that, with a discount rate of 5 percent, the net present value of a
hydroelectric plant with a life of 70 years is $25.73 million and that the net present value of a
thermal electric plant with a life of 35 years is $18.77 million. In the absence of information
about the future, we would calculate the net present value of the thermal plant by rolling over the
value twice to match the life of the hydroelectric plant. Proceeding in this manner would yield
the following net present value
($18.77 million) + ($18.77 million)/(1+0.05)35 = $22.17 million
However, suppose we have the following information about the future. Assume that at the end
of the first 35 years, there will be an improved second 35-year plant. Specifically, there is a 30
percent chance that an advanced solar or nuclear alternative will be available that will increase
the net benefits by a factor of three, a 60 percent chance that a major improvement in thermal
technology will increase net benefits by 50 percent, and a 10 percent chance that more modest
improvements in thermal technology will increase net benefits by 10 percent.
Using the information we have about possible future events, should the hydroelectric or thermal
plant be built today?
The present value of the hydro plant remains $25.73 million. The expected present value of two
successive 35-year plants is now calculated as follows:
PV(2 35-year plants) = ($18.77 million) +
{[(.3)(3)+(.6)(1.5)+(.1)(1.1)]($18.77 million)}/(1+.05)35
= $26.29 million
Thus, taking account of the possible improvements in technology, the 35-year thermal plant has a
larger expected present value of net benefits than the 70-year hydro plant.
5.) Imagine that we want to value a cultural festival from the point of view of a risk-averse
person. The person’s utility is given by U(I) where $I is her income. She has a 50 percent
chance of being able to get vacation time to attend the festival. If she gets vacation time, then
she would be willing to pay up to $S to attend the festival. If she does not get the vacation time,
then she is unwilling to pay anything for the festival.
a.) What is her expected surplus from the cultural festival?
ES = (.5)(S) + (.5)(0) = .5S
b.) Write an expression incorporating her option price, OP, for the festival if the festival takes
place.
(.5)U(I+S-OP) + (.5)U(I-OP) = EU0
where the first term on the left-hand side of the equation is the probability of attending times the
utility of attending, taking account of the certain payment; and the second term is the probability
of not attending times the utility obtained if not attending, taking account of the certain payment.
The right-hand side of the equation is the expected utility if there is no festival.
c.) Manipulate the expression for option price to show that the option price must be smaller than
her expected surplus (In doing this, begin by substituting 0.5S – e for OP in the equation derived
in part b. Also keep in mind that because the person is risk averse, her marginal utility declines
with income.)
Rewriting:
2U(I) = U(I+S-OP) + U(I-OP)
Substituting .5S - e for OP into the right-hand side of the equation gives:
2U(I) = U(I+S-.5S+e) + U(I-.5S+e)
U(I) = [U(I+.5S+e)+ U(I-.5S+e)]/2
Because the marginal utility of persons who are risk averse must decline with income, it is
apparent that the above equation could not hold for e=0. The gain from increasing income by
.5S would be smaller than the loss from decreasing income by .5S. The equation can hold only
when e is positive. Thus, option price must be smaller than the expected surplus. The option
value, OP-ES = -e, which, because e is positive, is negative.
6.) (15 points total) Suppose we have an efficiently operating market for good X (our primary
market good). Also, consider two secondary markets for goods Y and Z. X and Y are
substitutes for each other, while X and Z are complementary to each other.
Now assume the government imposes a tax of tx per unit of good X.
a.) Suppose the supply schedule in the market for good Z is perfectly elastic and this market
operates efficiently. Do we count changes in surplus that occur in the market for good Z (due to
the tax in the primary market) in our welfare analysis of the primary market? Why or why not?
Keep your answer to a sentence or two.
No, all changes are accounted for already in the primary market. We do not want to double
count the increase in consumer surplus.
b.) Suppose the supply schedule in the market for good Y is upward sloping. Furthermore,
suppose there exists a government maintained price support (aka price floor) in this market.
Illustrate graphically what happens in this market when the tax in the primary market is
imposed (assume the demand for good Y shifts such that the price floor is still binding). Do we
count any changes in this secondary market in our welfare analysis of the primary market?
-We do not count changes in consumer surplus (already accounted for)
-Producer surplus in the secondary market does not change.
-BUT, the DWL gets smaller…and this is a change that we would want to count!
4
7.) (15 points total)
Consider the following decision tree (□: decision node. ○: random selection of state of nature)
10
1st
year
P1
2nd
year
P3
P4
Option C
6
8
P2
1-P3 - P4
Option A
1- P1 - P2
10
C0
C0
Option D
Option B
6
Option E
1-P1 - P2
7
P3
P4
C0
P2
9
1 - P3 - P4
P1
Option F
4
12
2
8
The above decision tree represents a two period game where you (as a policy-maker) must
decide between several combinations of policies. The values given represent benefits. So, for
example, if you choose option A in the first period, then you stand to gain the following benefits:
$10 (with probability P1), $8 (with probability P2), or you carry on to period 2 (with probability
of 1 – P1 – P2). There are four possible policy combinations you have to choose from: (A, C);
(A, D); (B, E); (B, F). Given the following parameters, which option yields the greatest expected
net benefits?
•P1 = 0.2
•P2 = 0.6
•P3 = 0.4
•P4 = 0.4
•C0 = 3 (This represents a cost that you must incur if you choose options A, C, or E)
•Assume a discount rate of 0.10.
Option BE should be chosen