Download Midterm Exam 2 (W2014)

ECO 5520/6520 – Exam 2
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Midterm Exam 2 – ECO 5520/6520
Instructions
This examination has five questions and you are to do all five in a bluebook that you
provide, or on the exam sheet. Please number your answers clearly. Each question will be worth
20 points, and each part of each question will be weighted as indicated, so allocate your time
accordingly. The exam is “closed book – closed notes.” You may use a calculator.
You will have until from 12:50 until 2:40 to complete the exam. Latecomers will not be
given extra time to finish the exam. If you are unsure of a question, indicate what assumptions
you are making and go forward.
1. Suppose that there are 50 houses in the community with 2,000 square feet (ordinarily renting
for $8,000 per year), and another 150 houses in the community with 3,000 square feet
(ordinarily renting for $12,000 per year). The interest rate is 4% and with proper maintenance
all of the houses are expected to last forever. In an election the population decides that they
want public services worth $8,000 per year.
a. (5 points) What property tax rate will be necessary to fund these public services?
b. (5 points) How much money will be raised by the property tax rate?
c. (5 points) Calculate the value of the big houses after the tax is imposed?
d. (5 points) Calculate the value of the small houses after the tax is imposed?
ANSWER
a.
Small houses $200,000; Big houses $300,000. Base = 0.75*300 + 0.25* 200 = 275; Tax
rate = t = 8000/275,000 = 2.91%
b. $1,600,000
c. [(25*12)+(25*8)]/(1+25*0.0291) = 289.43
d. [(25*8)+(25*8)]/(1+25*0.0291) = 231.55
ECO 5520/6520 – Exam 2
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2. Consider the demand and supply of smart phones. They are given by the following equations.
PD = 800 – 12 QD
PS = 100 + 8 QS
a. (5 points) Calculate the equilibrium levels of price and quantity in this market.
b. (5 points) If a 10% tax is placed on the smart phone sellers, what will happen to the
equilibrium price and quantity, and tax revenues? Be specific with your answers.
c. (5 points) How much of the tax will be borne by buyers, and how much by sellers? Why?
d. (5 points) Calculate the “dead-weight” loss of the tax. Explain why this is a loss to society.
ANSWER
a. P* = 380
; Q* = 35
b. Price will rise; Quantity will fall. P* = 401.92; Q = 33.17; tax = $36.53/phone; Total tax
= 1212.09
c. Buyers will pay 401.92 – 380 of tax = 21.92; Sellers will pay $14.61
d. DW = 0.5* 36.56 * (35 – 33.17) = 33.38
ECO 5520/6520 – Exam 2
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3. Mr. Paravano presented a discussion of fixing Michigan’s roads. Use the accompanying
diagram for your answer.
MC with congestion – Answer d
$
CS
Costs
0
MB
MC1
MC2 – Answer c
Traffic
a. (5 points) What principle determines the optimal quantity of roads?
b. (5 points) Show the equilibrium with Michigan’s current roads. Indicate costs to the
drivers, and the consumer surplus.
c. (5 points) Show what happens with road improvements. Indicate the new equilibrium, and
the new level of consumer surplus.
d. (5 points) This diagram has been drawn without any road congestion. Show what happens
to costs when there is traffic congestion and explain why.
ANSWER
a.
b.
c.
d.
MB = MC
See graph
MC falls. CS increases
See graph. Increasing numbers of cars slow each other down.
ECO 5520/6520 – Exam 2
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4. Consider a municipality with particular preferences for Education and for Pizza. Both are
measured in dollars.
Pizza
a. (5 points) What is the slope
of the budget constraint, and why?
Answer to b
b. (5 points) Draw a graph showing
the impact of a grant of $E that can
be spent only on education.?
c. (5 points) Suppose, instead
that the state matches every $1 that
the municipality spends with $3.
In this case, what is the cost of the
grant?
d. (5 points) Suppose that as a
condition for receiving the grant
in part c, that the state requires
that the municipality spend
at least half of its funds on
education. Draw this condition and
explain how it may (or may not)
change your answer to part c.
Answer to d
Answer to c
0
50%
Education
ANSWERS
a. -1. Output is measured in dollars. You use a dollar on one or the other.
b. See graph – Horizontal line.
c. Slope -4.0. 1:1 + a 3 dollar match
d. See graph – Decrease in utility
ECO 5520/6520 – Exam 2
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5.
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S+R+A
90
$
This diagram is drawn to scale so you can use it to
answer Question 5 if you wish.
60
30
MC = 40
S+R
30
DA
0
6
DS
12 18
24
36
Quantity of tennis courts = Q
5. Please answer the following questions about public goods.
a. (5 points) Suppose that Adam and Steve both want tennis courts in their suburb. Adam’s
demand curve is DA, and Steve’s demand curve is DS. Draw the appropriate marginal
benefit curve that summarizes the demand for a public good for the two of them on the
graph above. Discuss briefly how you did it.
b. (5 points) What principle would you use to estimate the optimum amount of this local
public good? Is it the same or different as that used for private goods?
c. (5 points) If the marginal cost per unit of a tennis court is 40, show the optimal number of
tennis courts, based on your answers to parts (a) and (b). Give your best estimate, either
geometrically or algebraically.
d. (5 points) Steve has a twin sister Rosamunde, who has identical demand as Steve. What
will happen to your answers to parts a, b, and c, if Rosamunde moves into the town and
expresses her demands. Why?
ECO 5520/6520 – Exam 2
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ANSWERS
a. Draw and explain.
b. Sum of MB = MC
c. Looks like 10 – 11 tennis courts. Algebraically:
30 – 2.5Q + 60 – 2.5Q = 40
90 – 5Q = 40 ; Q* = 10
d. Shift up again by 60 – 2.5Q. Up to 12, it is 150 – 7.5Q = 40. Past 12, it is
120 – 5Q = 40; Q* = 16.