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Economics 115b
Introductory Economics
Spring 2006
George Hall and Staff
Problem Set 3 Solutions
1. Obviously, this question is open to multiple interpretations; there is no uniquely correct
answer. With this in mind, one should note that cell phones and meeting with friends can
be considered somewhat complementary because cell phones allow for spontaneous meetings
and run-ins that would not be possible without the connectivity that they provide. However,
the two goods may be considered substitutes because the dependence upon cell phones often
leads to less planning ahead and makes it easier to put off actual face-to-face meetings.
More generally, information technology advances have effects similar to those of cell phones.
Instant messaging, for example, leads to less face-to-face interaction as online chatting replaces
the need to physically meet with others in order to communicate. However, being more
connected often leads to more interaction within a group of friends, as well as opening the
door to the possibility of meeting more new people.
2. Recall that the linear demand curve is characterized by the formula Q = a−bP, implying that
the price elasticity of demand is equal to one at the midpoint of the demand curve (where
a
Q = a2 and P = 2b
). Therefore, to the right of this midpoint, demand is inelastic, while to
the left of the midpoint, demand is elastic.
(a) Attempts by the Colombian army to stop the flow of illegal drugs into the US imply
that there is an inward (leftward) shift of the supply curve. This leads to an increase in
equilibrium price and decrease in equilibrium quantity. Since drug dealers have benefited,
this implies that the price increase outweighs the quantity decrease; hence, the supply
shift must have occurred along the inelastic portion of the demand curve.
a
P
a
b
S
S
a
2b
P2
P1
D
a
2
Q
Q2
Q1
a
(b) New stadium construction implies that there is an outward (rightward) shift of the supply
curve. This leads to a decrease in equilibrium price and an increase in equilibrium
quantity. Since total revenue has increased, this implies that the quantity increase
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Economics 115b
Introductory Economics
Spring 2006
George Hall and Staff
outweighs the price decrease; hence, the supply shift must have occurred along the
elastic portion of the demand curve.
b
P
a
b
S
S
P1
P2
a
2b
D
Q1
Q
a
Q2 2
a
(c) A fall in the price of engines implies that there is an outward (rightward) shift of the
supply curve. This leads to a decrease in equilibrium price and an increase in equilibrium
quantity. Since total revenue has decreased, this implies that the quantity increase is
outweighed by the price decrease; hence, the supply shift must have occurred along the
inelastic portion of the demand curve.
c
P
a
b
S
S
a
2b
P1
P2
D
a
2
Q
Q1
Q2
a
3. Suppose that we know how responseive the spread of diseases like HIV/AIDS is to the price
of sterile needles, as well as how responsive drug use is to the price of sterile needles, and
consider a proposal the provide sterile hypodermic needles free of charge in cities with high
drug use.
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Economics 115b
Introductory Economics
Spring 2006
George Hall and Staff
(a) If the price elasticity of demand for sterile needles is high, then there will be a marked
increase in the use of sterile (as opposed to shared) needles, decreasing the transmission
rates of diseases like Hepatitis and HIV/AIDS. If the cross-price elasticity between drugs
and sterile needles is low, furthermore, this decrease in disease transmission will not be
accompanied by a significant increase in the number of drug users.
(b) If, on the other hand, the price elasticity of demand for sterile needles is low, then the
policy will not be very useful; there will not be a significant change in disease transmission
rates. Furthermore, if the cross-price elasticity between drugs and sterile needles is high,
the policy will be disasterous, as it will serve only to subsidize increased drug use.
4. The two goods that Janelle and Brian are choosing between are dollars spent on styling and
dollars spent on gas mileage; the price of one unit of each good is therefore one dollar. Thus,
each of Janelle and Brian faces a budget line given by the equation S + G = 20, 000, where S
represents dollars spent on styling and G represents dollars spent on gas mileage.
Since Janelle does not care at all about styling, we know that her indifference curves are
vertical lines (when S is on the vertical axis and G is on the horizontal axis). Therefore,
her most preferred bundle of mileage and styling on the budget line will have her spending
$20, 000 on gas mileage and $0 on styling.
S
Janelle
20000
G
20000
On the other hand, Brian cares equally about G and S. Therefore, his indifference curves will
be bowed towards the origin, and will be symmetric about the 45◦ line. Therefore, his most
preferred bundle of mileage and styline will have him spending $10, 000 on gas mileage and
$10, 000 on styling.
Alternately, one may interpret Brian’s preferences as viewing G and S to be perfect complements, in which case his indifference curves will be right-angles along the 45◦ line. Again, his
most preferred bundle of mileage and styling will have him spending $10, 000 on gas mileage
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Economics 115b
Introductory Economics
Spring 2006
George Hall and Staff
and $10, 000 on styling.
S
Brian Case 1
S
20000
20000
10000
10000
10000
G
20000
Brian Case 2
10000
G
20000
5. We will suppose that Anne’s travel budget is $50, 000, which can be spent on some combination
of train miles and plane miles. We will also suppose that train miles cost exactly $1 each,
while plane miles cost $1 for the first 25, 000 miles, $0.75 for the next 25, 000 miles, and $0.50
for all other miles. Therefore, if Anne spends all of her budget on train miles, she will be able
to purchase 50, 000 miles. Her budget line will have a slope of −1 for the first 25, 000 plane
miles, will then have a slope of −0.75 for the next 25, 000 plane miles, and will then have a
slope of −0.5 until it hits the horizontal axis. This intercept (where all money is spent on
plane miles) will be at 62, 500 miles ($50, 000 = $1×25, 000+$0.75×25, 000+$0.50×12, 500).
Train
50000
Slope 1
25000
Slope 0.75
6250
Slope 0.5
25000
Plane
50000 62500
6. Letting N and U represent new and used books, respectively, we know that Antonio’s original
purchase bundle was 5 units of N and 0 units of U. Since PN = $80 and PU = $50, this implies
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Economics 115b
Introductory Economics
Spring 2006
George Hall and Staff
that Antonio’s original income is $400. The price change, however, leads to increases in prices
and income – we have PN = $88, PU = $52.50, and I = $440.
(a) Notice that, relative to his income, the price of new books has remained the same – both
have increased by 10%. However, the price of used books increased by only 5%, making
them relatively cheaper. Therefore, the new budget line has the same intersection with
the vertical axis, but is less steep – it has rotated outwards about that vertical intercept.
N
5
4
3
New Budget Line
2
Old Budget Line
1
U
2
4
6
8
(b) Antonio is better off after the price change – his old consumption bundle is still available,
but he is now able to afford bundles that were beyond his means before the change in
prices.
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