ECONOMICS 108 First Midterm Fall, 1999
University of Rochester Alan C. Stockman
BEFORE YOU BEGIN: On the front page of your answer book, (1) PRINT YOUR NAME; (2) SIGN YOUR NAME; (3) Print your SOCIAL SECURITY NUMBER. The exam has 100 points, indicated in parentheses after each question. You have 60 minutes (9:55 until 10:55 sharp).
1. Mike can explain "marginal cost" in 12 minutes or can hypnotize a woman in 2 minutes. Steve can explain "marginal cost" in 20 minutes or hypnotize a woman in 3 minutes. Who has a comparative advantage in explaining marginal cost? in hypnotism? (4)
Mike has a comparative advantage in explaining MC.
Steve has a comparative advantage in hypnotism.
Reasoning -- Mike opportunity cost of explaining MC is lower than Steves -- Mike's is 12/2 = 6 hypnotized women (per explanation of MC), whiles Steve's is 20/3 = 6.67 > 6 hypnotized women (per explanation of MC). Once you know this, you automatically know that Steve has the comparative advantage in hypnotism. (To see why, note that Steve's opportunity cost of hypnotism is 3/20 (explanations of MC per woman hypnotized), while Mikes is 1/6 =3/18 > 3/20.)
2. Your company's marketing department estimates that the elasticity of demand for your company's product is (minus) 0.25. What happens to the quantity sold and total revenue if you raise the price by 10%? (2)
The quantity demanded falls by 2.5 percent. Total revenue rises (by 7.5%).
Reasoning --
The elasticity means that 0.25 = % change in quantity demanded per % change in price. Or:
0.25 = (% change in QD)/ (% change in price), so
0.25 = (% change in QD)/ (10%), so (0.25) (10%) = % change in QD, or
% change in QD = 2.5%.
Since your price rises by 10% and the quantity you sell falls by only 2.5%, your total revenue (which equals price times quantity sold) rises. (In fact, it rises by 10% - 2.5% = 7.5%.)
3. A newspaper said: "Increased retail demand for roasted and ground coffee because of lower prices... has contributed to a higher price for coffee." What's wrong with this reasoning? (4)
It confuses a change in the quantity demanded with change in demand.
In other words, it confuses a movement along a demand curve (due to a change in price) with a shift in the demand curve, which would cause a change in price. (See pages 76-7.)
4. True or false? Explain why. (2 points each)
(a) If Coke and Pepsi are substitutes, a rise in the price of Coke reduces the demand for Pepsi.
(b) An increase in the supply of a product with inelastic demand raises consumer spending on the product.
(a) False. A rise in the price of Coke raises the demand for Pepsi, because they are substitutes. (See page 79.)
(b) False. The increase in supply reduces consumer spending when demand is inelastic. (See Figure 2 on page 106.)
5. Explain the logic behind the claim that stock prices follow a random walk. (4)
If stock prices sometimes increased or decreased in a predictable way (aside from their trend increases), then (a) when people predict a future increase in stock prices, they would try to buy the stock now, before its price rises, to profit from the predictable increase. As people did this, demand for the stock would increase now, raising the price today until there are no longer profits to be made (that is, until there is no longer any predictable future increase in stock prices (aside from trend). Similar reasoning applies if people predict a future fall in stock prices -- they would try sell the stock (or short-sell it) today, before its price falls, to profit (or avoid losses) from the predictable fall. As people did this, demand for the stock would fall now, reducing the stock price today until there is no longer any predictable future fall in stock prices.
6. Draw graphs to show:
(a) how a maximum legal price (below the equilibrium price) would affect equilibrium output. (3)
(b) how a minimum legal price (above the equilibrium price) would affect equilibrium output. (3)
(c) how a maximum legal price (below the equilibrium price) on computer chips would affect the price of computers. (3)
(a) Output would decrease. See Figure 1 on page 180.
(b) Output would decrease. See Figures 4 or 5 on pages 186-7.
(c) The price of computers would increase. See Figure 3 on page 185 -- and replace "peanuts" with "computer chips" and "peanut butter" with "computers."
7. If the interest rate is 10 percent per year, approximately what is the discounted present value of:
(a) $3000 paid one year from now? (2)
(b) $3000 paid 2 years from now? (2)
(c) $3000 paid every year forever? (2)
(d) a prize that pays $3000 one year from now and an additional $3000 five years from now? (2)
(a) $3000/1.10
(b) $3000/(1.10)2 = $3000/1.21
(c) $3000/0.10 = $30,000
(d) $3000/1.10 + $3000/(1.10)5
8. Suppose the government cuts taxes and thereby creates a budget deficit. Draw a graph to show how this deficit affects (a) total U.S. borrowing from other countries, and (b) the interest rate (6)
The answer to this question is shown in Figure 10 on page 171.
(a) U.S. borrowing would increase.
(b) The interest rate would increase.
9. Suppose the government announces a new program to pay half of college tuition for any full-time student. Use a graph to help explain how this program is likely to affect the (a) tuition per student that colleges collect, (b) the cost to students of going to college, and (c) the total tuition revenue that colleges collect. (6)
Here college admission is the product
and tuition is the price.
(a) Colleges are sellers.
The subsidy raises the tuition that they collect per student.
(b) Students are buyers.
The subsidy lowers the tuition that they each pay.
(c) The subsidy raises college tuition revenue, because it raises BOTH per-student tuition that the college collects AND the number of students.
10. (15) New York City limits the number of taxicabs on the streets by requiring that taxis have licenses called medallions. The city limits the number of medallions in existence. People can legally buy and sell medallions. (a) Draw graphs to help explain the price of medallions. (b) Explain, using a graph, how changes in the demand for taxi rides affects the price of medallions. (c) What would happen to the price of a medallion if the government required taxi companies to provide free accident insurance for people who ride in taxis?
(a) Draw equilibrium of supply and demand for medallions. The supply is limited by the city (perhaps perfectly inelastic). The demand for medallions depends on the discounted present value of future profits that you could earn by owning a medallion and being in the taxi business. The higher the discounted present value of those future profits, the higher demand for medallions (the greater the willingness to pay for them).
(b) An increase in the demand for taxi rides raises the equilibrium price of those rides. This raises the discounted present value of profits from operating a taxi, so it raises the demand for medallions. (Opposite, of course, for a decrease.)
(c) (This is a more complicated problem. ) This requirement would raise the marginal cost of providing taxi rides. Therefore it would reduce the profits from operating taxis. For this reason, it would decrease demand for medallions, reducing the price of medallions.
You might be tempted to argue that there is a second, offsetting effect at work. A firm's marginal cost curve is its supply curve (as long as it does not shut down). So the increase in marginal cost decreases supply of taxi services, raising the price of taxi services and tending to raise profitability of the taxi business. However, the price of taxi services will rise by less than the marginal cost of providing them. To see why, notice that the government regulation that forces taxi companies to provide free insurance to riders is like a tax on taxi rides -- the effects are the same as if the government placed a tax on taxi rides, and used the tax revenue to buy insurance for the riders. A tax on a good reduces profit (except in the extreme cases in which either demand is perfectly inelastic or supply is perfectly elastic). So this requirement, like a tax, reduces profitability of the taxi business and reduces the demand for medallions, lowering their price.
11. (6 points) Pam sells pumpkins for $5 each. The table shows Pam's cost of producing pumpkins. How many pumpkins should she produce to maximize her profit? Why?
|
number of pumpkins |
Total cost |
Marginal cost per 1000 pumpkins |
Marginal Revenue per 1000 pumpkins |
Total Revenue |
Profit |
|
1000 |
$3000 |
$3000 |
$5000 |
$5000 |
|
|
2000 |
$4000 |
$1000 |
$5000 |
$10,000 |
|
|
3000 |
$5000 |
$1000 |
$5000 |
$15,000 |
|
|
4000 |
$6500 |
$1500 |
$5000 |
$20,000 |
|
|
5000 |
$9000 |
$2500 |
$5000 |
$25,000 |
|
|
6000 |
$12000 |
$3000 |
$5000 |
$30,000 |
|
|
7000 |
$16000 |
$4000 |
$5000 |
$35,000 |
|
|
8000 |
$21000 |
$5000 |
$5000 |
$40,000 |
$19,000 |
|
9000 |
$27000 |
$6000 |
$5000 |
$45,000 |
|
Produce 8000 pumpkins, because at that quantity her MR = MC (marginal revenue equals marginal cost).
12. (17 points total)
(a) (3 points) Suppose the demand curve for tickets to a college rock concert is
QD = 250 - 2P
and the supply curve is QS = 5 + 3P
where QD is the quantity demanded, QS is the quantity supplied, and P is the price in dollars. Find the equilibrium price and quantity.
Qd = 250-2P Qs = 5 + 3P
so 250-2p=5+3p
or 245=5p
so p=$49
and Q=5+49*3=5+147=152 (or Q=250-2*49= 250-98 = 152.)
(b) (3 points) Suppose 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.
Tax=10, so pb = ps + $10,
where pb is the gross price buyers pay and ps is the net price sellers receive.
So 250-2(ps+10)=5+3ps
or 225=5ps
or ps=$45, pb=$55
Q=250-110=140 (or Q=5+3*45=140)
The tax reduces consumer surplus by area B+C. It also reduces producer surplus by area D+E.
The tax creates government revenue of B+C+D+E. And it creates a deadweight social loss of C+E.
In this problem, part (a) showed that P1 =$49 and Q1=152.
Part (b) showed that Pb=$55, Ps=$45, and Q2=140. So:
|
Area B |
= $840 |
Because it is a rectangle with height Pb-P1 = $55-$49 = $6 and base Q2 = 140. So its area is ($6)(140) = $840 |
|
Area C |
= $36 |
Because it is a right triangle with height Pb-P1 = $55-$49 = $6 and base Q2-Q1 = 152-140 = 12. So its area is ($6)(12)/2 = $36 |
|
Area D |
= $560 |
Because it is a rectangle with height P1 - Ps = $49-$45 = $4 and base Q2 = 140. So its area is ($4)(140) = $560 |
|
Area E |
= $24 |
Because it is a right triangle with height P1 - Ps = $49-$45 = $4 and base Q2-Q1 = 152-140 = 12. So its area is ($4)(12)/2 = $24 |
So the tax:
(d) (3 points) Suppose the student government subsidizes purchases of tickets by $10 per ticket (the student government pays $10 per ticket to buyers). Find the equilibrium price paid by buyers, price received by sellers, and quantity bought and sold.
Subsidy = 10, so ps = pb + 10 (or pb = ps - 10)
where pb is the net price buyers pay and ps is the gross price sellers receive.
So 250-2pb=5+3pb+3*10
or 215-2pb=3pb
or 215=5pb
So pb=43, ps=53,
Q=250-2*43=164 (or Q=5+3*53=164)
(e) (4 points) How does the subsidy in part (d) affect consumer surplus? producer surplus? How much money does the subsidy cost the student government? How large is the deadweight social loss from the subsidy?
The subsidy raises consumer surplus by area F+E. It also raises producer surplus by area B+C.
The subsidy costs the government B+C+D+E+F. The subsidy creates a deadweight social loss of D.
Notice that:
|
Area B + the part of area C to the left of Q=152 |
= $912 |
Because it is a rectangle with height Ps-P1 = $55-$49 = $6 and base 152. So its area is ($6)(152) = $912 |
|
the part of Area C to the right of Q=152 |
= $36 |
Because it is a right triangle with height $55-$49 = $6 and base 164-152 = 12. So its area is ($6)(12)/2 = $36 |
|
Area F + the part of area E to the left of Q=152 |
= $608 |
Because it is a rectangle with height $49-$45 = $4 and base 152. So its area is ($4)(152) = $608 |
|
the part of Area E to the right of Q=152 |
= $24 |
Because it is a right triangle with height $49-$45 = $4 and base 164-152 = 12. So its area is ($4)(12)/2 = $24 |
|
Area D |
= $60 |
Because it is a triangle with height $10 and base 164-152 = 12. So its area is ($10)(12)/2 = $60 |
So the subsidy:
13. (15 points) Microogulators are storable at zero cost, but they can become damaged by small particles in the air during storage. Usually, only about half of all microogulators are usuable after being stored for one year. (The other half become worthless.) Several major European firms just announced that they will expand their operations next year, which require microogulators as inputs. Consequently, the demand for microogulators is expected to triple between now and next year. Use graphs to help explain how these developments are likely to affect (a) the current price of microogulators, (b) next year's price of microogulators, (c) current production of microogulators, (d) future production of microogulators, (e) current consumption of microogulators, and (f) future consumption of microogulators,
This is a problem in speculation. The key thing to notice is that only half of the goods put into storage today are available to come out of storage next year. So, for example, if you put 100 microogulators into storage, only 50 will come out of storage next year. Suppose the equilibrium price today were $10,000 per microogulator. Speculators must sacrifice $20,000 today for every one microogulator that they sell next year. Consequently, the equilibrium works as if storage were costly.
Except for that feature, this is a straightforward speculation problem. The new equilibrium will look similar to like the one in Figure 8 on page 169, except that the numbers are different and only half of the goods stored today come out next year. So a graph of this situation (not to scale) would look like this:
As the graph shows, this increase in future demand: