Name/perm #_______________________________________________________________________
Econ 130
Test 3
John Hartman
December 11, 2012
Instructions:
You have 140 minutes to complete this test, unless you arrive late. Late arrival will lower the time available
to you, and you must finish at the same time as all other students.
Each question shows how many points it is worth. Show all work in order to receive partial credit for correct
work in some cases. Clearly circle your answer(s) or else you may not receive full credit for a complete and
correct solution.
Cheating will not be tolerated during any test. Any suspected cheating will be reported to the relevant
authorities on this issue.
You are allowed to use a nonprogrammable four-function or scientific calculator that is NOT a
communication device. If you use a calculator that does not meet these requirements, you will be assumed to
be cheating.
Unless otherwise specified, you can assume the following:
 Supply curves have positive slope and demand curves have negative slope.
 Negative quantities cannot be supplied or demanded.
 Negative prices are not possible.
You are allowed to turn in your test early if there are at least 10 minutes remaining. As a courtesy to your
classmates, you will not be allowed to leave during the final 10 minutes of the test.
Your test should have 8 questions, worth a total of 70 points. If your test is incomplete, it is your
responsibility to notify a proctor to get a new test.
For your reference, an example of a well-labeled graph is below:
Combined value of 2 shares & 1 put ($)
This part
has slope 2
$80
B
This part has slope 1
$40
A
Value of stock @
expiration ($)
$40
1. (4 points) Suppose hypothetically that you are working for a local school district. Someone shows you that
college graduates earn 84% more than high school graduates. Your boss wants you to start counseling belowaverage students that are on track to graduate high school. You are told that you should explain to these
students that they will earn 84% more if they enroll in college. Do you believe this? Use the material from
this class to explain your answer in 50 words or less. (Note: Be careful what you write. If you write anything
incorrect, you will lose credit for an otherwise correct answer.)
This is probably not believable. There are many reasons that you could have mentioned (key words
underlined):
 A greater drop in marginal returns for below-average students.
 This statistic may be causal on college-bound students, but probably not on others.
 Below-average students may not be able to signal they are hard-working, leading to it being
impossible to finish college.
2. (5 points) There are two routes between Aaronsville and Juliasville, and 150 cars must travel between
these two towns. One route is La Paz Avenue, in which anyone traveling on this route has a travel time of 70
minutes. The other route is Jefferson Highway, in which the travel time depends on the number of travelers
on the highway. The travel time on the highway is 20 + T, with T representing the total number of drivers on
the highway. What is efficient if you are trying to minimize the total number of minutes of travel time of all
travelers? Make sure to state the number of travelers on each route.
Minimize T(20+T) + (150-T)70, or T2 – 50T +10500. Take the first order condition and set it equal to 0:
2T – 50 = 0  T = 25. So there are 25 on Jefferson HW and 150 – 25, or 125, on La Paz Ave.
3. Agusta has a utility function of U(I,L) = IL, with I representing dollars of annual income this year (after
cash transfers and taxes are applied, if applicable), and L representing hours of leisure this year. Agusta can
work as many hours as she wants for $14 per hour. Assume that Agusta has 4000 hours this year for work,
leisure, or a combination of the two. (Note: On this problem, you need to justify your answer completely to
get all points.)
(a) (4 points) Without any government assistance programs or taxes, how many hours will Agusta work this
year?
U(I,L) = IL = (14W)(4000-W) = 56,000 – 14W2
Take the first order condition and set it equal to 0: 56,000 – 28W = 0  W = 2,000
(b) (7 points) If the government offers a $10,000 cash transfer to anyone who receives $24,500 or less in
income from working this year, how many hours will Agusta work this year?
U(I,L) = IL = (14W+10,000)(4,000-W) = 40,000,000 + 46,000W – 14W2
Take the first order condition and set it equal to 0: 46,000 – 28W = 0  W = 1,642.86
Next, we need to compare the utility here with the utility in part (a).
From (b), U(33,000, 2357.14) = 77,785,714
From (a), U(28,000, 2,000) = 56,000,000
So, choose the higher utility calculated from (b).
Note: If you picked to work to receive $24,500 in income from working, your utility would be lower than the
highest utility possible: U(34,500, 2,250) = 77,625,000
(c) (8 points; this part is meant to be difficult) Suppose that the cash transfer is no longer available. Instead,
the government will tax Agusta as follows: No taxes are imposed for the first $7,000 earned per year, a
marginal tax rate of 15% is imposed for the next $14,000, and a marginal tax rate of 35% is imposed for
every dollar earned after that. How many hours will Agusta work this year?
From part (a), it is clear that Agusta will work at least 500 hours this year.
If she works from 500-1500 hours this year, her utility is IL = [7,000 + 11.9(W-500)](4000 – W) =
4,200,000 + 46,500W -11.9W2. Take the first order condition and set it equal to zero: 46,550 – 23.8W = 0
 W = 1,955.88 (note that this leads to a contradiction, but tells us that W is at least 1500).
If she works more than 1500 hours this year, her utility is IL = [18,900 + 9.1(W-1500)](4000-W) =
21,000,000 + 31,150W – 9.1W2. Take the first order condition and set it equal to zero: 31,150 – 18.2W = 0
 W = 1,711.54 (THIS IS THE ANSWER!)
4. (10 points; this problem is meant to be difficult) Joanie and Johannes are wondering what to do with
educating their child, Joseph. The household is able to spend $100,000 total. The family’s utility function is
U(x,y) =xy9, where x represents $1000s spent on educating Joseph, and y represents $1000s spent on
everything else. Joanie and Johannes can choose to spend as much money on educating Joseph as they want.
However, if total spending on Joseph’s education is $8,000 or less, half of the money will be provided by the
government. In other words, if Joseph’s education spending is $8,000 or less, then only 50 cents of
household money has to be used for each dollar of Joseph’s education spending. What should Joanie and
Johannes do to maximize household utility? Justify your answer.
If x>8, then we need to solve max xy9 such that x+y = 100  max (100-y)y9, or max 100y9 – y10. Take the
first order condition and set it to zero: 900y8 – 10y9 = 0  y = 0 or 90 (ignore 0, since this gives a utility
minimum)  x = 10
If x<8, then we need to solve max xy9 such that x/2 + y = 100  max (200-2y)y9, or max 200y9 -2y10. Take
the first order condition and set it to zero: 1800y8 – 20y9 = 0  y = 0 or 90 (ignore both, but find the closest
to 90 that meets or condition of spending $8,000 or less on Joseph’s education: x= 8 and y=96).
Compare the two utilities: U(10,90) = 3.8742 * 1018 vs. U(8,96) = 5.5403 * 1018
Choose the second: x = 8, y = 96, due to having the higher utility.
5. Natalie is in the hospital from a fall during a concert. The total cost of having Natalie in the hospital is
8,000Q + 400Q2, with Q denoting the number of days in the hospital. Natalie’s total benefit of being in the
hospital is 20,000Q – 750Q2.
(a) (4 points) How long will Natalie want to stay in the hospital if she only has to pay a $5,000 co-payment?
Natalie’s MC is 0: Set Natalie’s MC = MB  0 = 20,000 – 1500Q  Q = 13.333
(b) (7 points) What is the deadweight loss (or excess burden) of your answer in part (a)? (Hint: You may
want to draw a well-labeled graph to help justify your solution.)
DWL = 0.5*8.115942*18,667 = 75,748.76
(see below)
$
18,666.67
This
triangle is
the DWL
Q
5.217391
13.333333
6. (5 points) Suppose you live with a personal income tax with the following structure: Adjusted Gross
Income (AGI) minus exemptions minus the standard deduction equals taxable income. Taxable income is
subject to the following marginal rates:
Official Statutory Tax Rate Schedule (2012)
Single Returns
Taxable Income
Joint Returns
Taxable Income
$0-$8,700
Marginal
Tax Rate
10%
$0-$17,400
Marginal Tax
Rate
10%
$8,700-$35,350
15
$17,400-$70,700
15
$35,350-$85,650
25
$70,700-$142,700
25
$85,650-$178,650
28
$142,700-$217,450
28
$178,650-$388,350
33
$217,450-$388,350
33
$388,350 and over
35
$388,350 and over
35
Suppose that each eligible family member results in an exemption of $3,800. The standard deduction is
$5,950 for a single return. The standard deduction is $11,900 for a joint return. If Beth and Mark have AGI
of $130,000 per year each, how much more will they pay in taxes if married filing jointly, relative to each
being single? Assume that there are no other members in this family except for Beth and Mark.
Single taxes (for each person): AGI = 130,000 – 3,800 – 5,950 = 120,250
Tax = .1(8,700) + .15(26,650) + .25(50,300) + .28(34,600) = 27,130.50
Joint taxes: AGI = 260,000 – 3,800(2) + 11,900 = 240,500
Tax = .1(17,400) + .15(53,300) + .25(72,000) + .28(74,750) + .33(23,050) = 56,271.50
The difference is 56,371.50 – 2(27,130.50) = $2,010.50
7. Suppose that the supply of dog biscuits is represented by the equation P = 2Q, while the demand is
represented by the equation P = 900 – Q. Assume that the dog biscuit market is competitive with no market
failures in the absence of a tax. (Note: Fractional numbers of dog biscuits are possible here.)
(a) (4 points) If there is a 15 percent ad valorem tax imposed on the gross price, how many dog biscuits will
be purchased? Assume that the tax is imposed on consumers.
New demand (D’ in the graph below in part (b)): P = .85(900 – Q) = 765 – 0.85Q.
Next, set 765 – 0.85Q = 2Q  Q = 268.42.
(b) (5 points) What is the excess burden (or deadweight loss) due to the tax? (Hint: A well-labeled graph
may help you with solving this question.)
$
S (MC)
900
The area of this triangle is the DWL:
0.5 * (300 – 268.42) * (631.58 – 536.84), or
DWL = 1,495.94
765
900
631.58
536.84
900
D (MB)
D’
Q
268.42
900
300
900
900
Note that to the calculation to find 300 on
the horizontal axis is as follows:
900 – Q = 2Q  Q = 300
8. (7 points) Let Q be the number of units of pollution reduction. Suppose that the government estimates
that marginal cost of pollution reduction is 1.5Q. The marginal social benefit of pollution reduction is 600 –
3Q. Suppose that firms will pollute 400 units without government regulation. What is the socially efficient
amount of pollution permits if the government decides to use a cap-and-trade system? (Note: Fractional units
of pollution are possible here.)
Let Q = pollution reduction units. Then 1.5Q = 600 – 3Q  Q = 133.33.
Let q = # of units of pollution, and q* the efficient quantity. Then q* =400 – 133.33 = 266.67