ECONOMICS 108 First Midterm Fall, 2000
University of Rochester Alan C. Stockman
BEFORE YOU BEGIN: On the front page of your answer book,
PRINT YOUR NAME;
SIGN YOUR NAME;
Print your SOCIAL SECURITY NUMBER.
The exam has 100 points. You have 75 minutes (2:00 until 3:15 sharp).
The number of points is indicated in parentheses (after each question number).
1. "True" or "false"? No explanation is required. (10 possible points -- a correct answer is worth one point, no answer at all is zero points, and an incorrect answer is minus one point. Therefore, you should guess only if you are sufficiently confident in your answer; otherwise, it is better not to answer.)
(a) Demand for a good is more elastic when close substitutes for it are available to buyers.
TRUE
(b) A maximum legal price (below the equilibrium price) reduces equilibrium output, and a minimum legal price (above the equilibrium price) raises equilibrium output.
FALSE
(c) The more inelastic the supply of labor, the greater wage increase when the demand for labor increases.
TRUE
(d) Reliable scientific studies show that people who use suntan lotion are more likely to develop skin cancer. It is reasonable to conclude from this fact that people should try to avoid using suntan lotion.
FALSE
(e) If Furbies and Beanie Babies are substitutes, then a tax on sales of Beanie Babies machines would raise the price of Furbies.
TRUE
(f) A 50-cent increase in the tax on cigarettes would raise the equilibrium price of cigarettes by 50 cents.
FALSE
(g) If the elasticity of demand for your company's product is (minus) 2 , then a 10% increase in price will reduce sales by 5%.
FALSE
(h) If Komex Corporation has a lower fixed cost than its competitors; but has the same variable costs and the same demand for its product, then Komex will produce more than its competitors.
FALSE
(i) If firms "overbuild" hotels in a city (building too many hotels so that many rooms are empty each night), the price of hotel rooms in that city will rise to make up for all the empty rooms.
FALSE
(j) Some changes in the economy are economically efficient but not Pareto improvements, but all Pareto improvements are economically-efficient changes.
TRUE
2. (3) Consider the data in the following table:
|
Hours of Work Required for: |
Robin |
Little John |
|
Making one
crossbow |
12 hours |
11 hours |
|
Making one
arrow |
2 hours |
2 hours |
(a) Who has the comparative advantage at making arrows? Robin
(b) What is Robin's opportunity cost of making a crossbow? 6 arrows
(c) What is Little John's opportunity cost of making a crossbow? 5½ arrows
3. (3) If the interest rate is 10% per year, what is the discounted present value of
(a) $100 paid one year from now? $100/1.10 = $90.90 (about $91 is a good enough answer)
(b) $100 paid two years from now? 
or about $82 or $83
(c) $100 paid every year, forever? $100/0.10 = $1000
4. (2) If the interest rate is 10% per year, what is the value of a firm that will have $1000 profit after one year and an additional $1000 profit after its second year (and no profits after that)?
This is the sum of the discounted present values of the profits in those years, or
(or about
$1730-$1740)
5. (4) Explain the logic behind the claim that stock prices follow a random walk.
If people expected the stock price to rise, they would profit by buying the stock now, before its price rises. As people try to do this, the stock price rises now, until the current price equals (roughly) the expected future price. Similarly, if they expected the price of a stock to fall, they would profit by selling (or short-selling) the stock now, before its price falls. As people try to do this, the stock price falls now, until the current price equals (roughly) the expected future price.
6. (4) Define (or explain) the marginal cost and marginal benefit of an action.
The marginal benefit of an action is the increase in total benefit when you do that action a little more. (Marginal benefit is the derivative of total benefit with respect to the quantity of the action.) The marginal cost of an action is the increase in total cost when you do that action a little more. (Marginal cost is the derivative of total cost with respect to the quantity of the action.)
7. (3) What is a sunk cost? Give an example.
A sunk cost is an amount that was previously a cost of an action, but is no longer the cost of any action you could take. For example, if you buy a ticket to a movie, the price of the ticket is part of the cost of seeing the movie. However, after you buy the ticket, you cannot get your money back. The ticket price then becomes a sunk cost and is no longer a relevant cost of any action you could take, such as staying to watch the movie, or leaving because the movie is lousy.
8. (5) People can reach the Island Restaurant only by boat. The round trip used to take one hour, but now it takes only 40 minutes. Draw a graph to show how this change affects the demand for meals at the Island Restaurant if all potential diners value their time at $12 per hour.
Buyers value the 20 minutes they save at $4, so the demand curve shifts upward by $4. In other words, the highest price that buyers are willing to pay for meals rises by $4 because buyers implicitly pay $4 less in a time price when they go to the restaurant. The equilibrium moves from point A to point B, so the price rises from P1 to P2. So the price rises, but it rises by less than $4 (less than the upward shift in the demand curve). SEE GRAPH BELOW.
9. (6) Explain how
and why an increase in the expected future demand for a product can
affect its price now.
(See Figure 6 on page 166 of the text.)
10. (7) You have final exams in Advanced Human Cloning
and Sexual Psychology of Robots.
You have only one more hour to study.
You want to maximize the total number of points you get on the two exams
added together. You expect the following scores, which depend on how much you
study each subject:
Minutes Expected Minutes Expected
Studying Score in Studying Score
in
Cloning Cloning Robot-Psych Robot-Psych
0 67 0 53
10 74 10 63
20 80 20 71
30 85 30 78
40 89 40 83
50 92 50 88
60 94 60 91
(a) Draw a table to show
your marginal benefit and marginal cost from studying cloning.
|
Minutes Studying Cloning |
Remaining Minutes to Study Robot-Psych (EQUALS 60 min.
minus time spent studying cloning |
Expected Score in Cloning |
Marginal Benefit of
extra time to study Cloning |
Expected Score in Robot-Psych
|
Marginal COST of extra
time to study Cloning (which is an opportunity cost that EQUALS the fall in
your expected score in Robot-Psych |
|
0 |
60 |
67 |
|
91 |
|
|
10 |
50 |
74 |
7 |
88 |
3 |
|
20 |
40 |
80 |
6 |
83 |
5 |
|
30 |
30 |
85 |
5 |
78 |
5 |
|
40 |
20 |
89 |
4 |
71 |
7 |
|
50 |
10 |
92 |
3 |
63 |
8 |
|
60 |
0 |
94 |
2 |
53 |
10 |
(b) How much should you study for each exam? Why?
You can’t do better than studying 30 minutes for each exam – because that
is the amount of studying for which marginal cost equals marginal benefit.
(c) If you had 70 rather than 60 minutes to study, how would this change your answers above? How many additional points could you expect to get by studying that extra 10 minutes?
In this case, modify the table starting with the second column, as follows:
|
Minutes Studying Cloning |
Remaining Minutes to Study Robot-Psych (70 min. minus time
spent studying cloning |
Expected Score in Cloning |
Marginal Benefit of
extra time to study Cloning |
Expected Score in Robot-Psych
|
Marginal COST of extra
time to study Cloning |
|
0 |
70 |
67 |
|
? |
|
|
10 |
60 |
74 |
7 |
91 |
|
|
20 |
50 |
80 |
6 |
88 |
3 |
|
30 |
40 |
85 |
5 |
83 |
5 |
|
40 |
30 |
89 |
4 |
78 |
5 |
|
50 |
20 |
92 |
3 |
71 |
7 |
|
60 |
10 |
94 |
2 |
63 |
8 |
|
70 |
0 |
? |
|
53 |
10 |
You can’t do better than studying 30 minutes for Cloning and 40 minutes for Robot-Psych, because marginal cost equals marginal benefit in that case. Your total score goes up by 5 points (on the Robot-psych exam).
11. (6) Draw a graph to show the effects of an income tax on
(a) wages paid by employers (firms) including taxes;
(b) wages received by employees (workers) net of taxes;
(c) employment;
(d) government revenue from the tax;
(e) the deadweight social loss from
the tax.
12. (6 points - 3 points each) Draw graphs to show:
(a) The effects of a tax on a product that has perfectly inelastic demand.
The tax raises the price paid by buyers, leaving unchanged the price received by sellers and the equilibrium quantity:
(b) The effects of a tax on a product that has perfectly inelastic supply.
The tax lowers the price received by sellers, leaving unchanged the price paid by buyers and the equilibrium quantity:
13. (14) Draw a graph to explain why a law that prohibits international trade would be economically inefficient. On your graph, show the effects of that law on prices and on quantities produced and consumed. Who would gain and who would lose from that law? Use your graph to show how much they would gain or lose.
The following graph shows that WITH international trade, the world equilibrium price $5. At that price, the U.S. produces 9 units per week, consumes 3 units, and exports 6 units. The other country produces 4 units, imports 6 units, and consumes 7 units. Consumer surplus in the U.S. is area A (in purple) and producer surplus in the U.S. is area B+C+D (in green and beige). Consumer surplus in the other country is area E+F+G (in purple, blue, and beige) and producer surplus in the other country is area H (in green).
A law that prohibits international trade leads to a $3 equilibrium price in the U.S., with an equilibrium quantity of 5. Consumer surplus in the U.S. becomes area A+B (in purple and light green), so consumers in the U.S. gain area B from the law. Producer surplus in the U.S. becomes area D (in dark green), so producers in the U.S. lose area B+C from the law. As a whole, then, the law transfers area B from U.S. producers to U.S. consumers, and causes a deadweight social loss of area C in the United States.
In addition, the law leads to an $8 equilibrium price in the other country, with an equilibrium quantity of 7. Consumer surplus in the other country becomes area E (in purple), so consumers in the other country lose area F+G from the law. Producer surplus in the other country becomes area F+H (in purple and dark green), so producers in the other country gain area F from the law. As a whole, then, the law transfers area F from foreign consumers to foreign producers, and causes a deadweight social loss of area G in the other country. (In total, the law causes a deadweight social loss of area C+G.)
In summary, the law prohibiting international trade has the following effects:
U.S. consumers gain B
U.S. producers lose B+C
foreign consumers lose F+G
foreign producers gain F
14. (5 points) The table shows part of a spreadsheet with
information on total cost and total revenue from selling various quantities of
product. On your answer sheet, write
down a table showing quantity, marginal cost and marginal revenue.
What quantity in the table maximizes profit?
|
Quantity |
Total cost |
Marginal cost |
Total Revenue |
Marginal Revenue |
|
6 |
$12000 |
$3000 |
$30,000 |
$5000 |
|
7 |
$16000 |
$4000 |
$35,000 |
$5000 |
|
8 |
$21000 |
$5000 |
$40,000 |
$5000 |
|
9 |
$27000 |
$6000 |
$45,000 |
$5000 |
The quantity 8 maximizes profit.
15. (22 points total)
Suppose the demand curve for tickets to a rock concert is
QD = 150 - 3P
and the supply curve is
QS = 2P -10
where QD is the quantity demanded (in thousands), QS is the quantity supplied (in thousands), and P is the price in dollars.
(a) (4) Find the equilibrium price and quantity. 150-3P=2P-10 therefore P=32 and Q=54
(b) (4) Find consumer surplus and producer surplus.
Draw a graph like the one below. The supply curve hits the vertical axis at a price of $5 (since the quantity supplied is zero if that is the price), and the demand curve hits the vertical axis at a price of $50 (since the quantity demanded is zero if the price is $50). Consumer surplus is area A+B+C, which is ½ ($50-$32)(54)=($18)(27)=$486. Producer surplus is area D+E+F, which is ½ ($32-$5)(54)=($27)(27)=$729.
$5 $26 $10 $36 42 $32 54 $50
(c) (3) Suppose that the government puts a $10 per ticket tax on sales of these tickets. Find the equilibrium price paid by buyers, price received by sellers, and quantity bought and sold.
Let PB= price buyers pay, and PS=price sellers
receive. Then 150-3PB=2PS-10, and
PB=PS+10.
Therefore 150-3(PS+10)=2PS-10 so PS=26, and PB=36. So Q=42.
(d) (4) By how much does the tax in part (c) increase or decrease consumer surplus? By how much does it increase or decrease producer surplus? How much money does the government collect from the tax? How large is the deadweight social loss from the tax?
Draw a graph like the one above. Consumer surplus with the tax is area A,
which is ½ ($50-$36)(42)=($14)(21)=$294.
Producer surplus with the tax is area F, which is ½
($26-$5)(42)=($21)(21)=$441. So
consumer surplus falls by $192 (=$486-$294), which is area B+C, i.e. it equals
(½)($4)(12) + ($4)(42) =$24+$168 = $192.
Similarly, producer surplus falls by 288 (=$729-$441), which is area
D+E, i.e. it equals (½)($6)(12) + ($6)(42) =$36+$252 = $288.
Total tax payments, which the government collects, is
area B+D, or ($10)(42)=$420. Since
consumers lose B+C and producers lose D+E, but the government gains only B+D,
area C+D shows the deadweight social loss from the tax. It equals (½)($10)(12) = $60.
(e) (3) Suppose that the government puts a $10 per ticket subsidy on sales of tickets. Find the equilibrium price paid by buyers, price received by sellers, and quantity bought and sold.
Let PB= price buyers pay, and PS=price sellers
receive. Then 150-3PB=2PS-10, and
PS=PB+10.
Therefore 150 - 3PB = 2(PB+10) -10 so PB=28, PS=38, and Q=66.
(f) (4) By how much does the subsidy in part (e) increase or decrease consumer surplus? By how much does it increase or decrease producer surplus? How much money does the subsidy cost the government? How large is the deadweight social loss from the subsidy?
Draw a graph like the one below. With the subsidy, consumer surplus is area
A+B+E+F, which is ½ ($50-$28)(66)=($11)(66)=$726, so consumer surplus rises by
$240. Producer surplus is area B+C+
F+G, which equals ½ ($38-$5)(66)=($33)(33)=$1089. So it rises by 360. The government spends ($10)66=$660 on the
subsidy, but the sum of the gains to consumers and producers is only $600. The difference, $60, is the deadweight
social loss, which is the area of D.
66 $5 $50 $28 $32 $38
