Economics 2
Spring 2017
Professor Christina Romer
Professor David Romer
SUGGESTED ANSWERS TO PROBLEM SET 1
1.a. The opportunity cost of a point on your economics exam is 2 points on your chemistry exam. It
takes 30 minutes of studying to raise your economics score by a point. But each 30 minutes that
you spend studying for your economics exam is 30 minutes that you’re not spending studying for
your chemistry exam, and those 30 minutes would have raised your chemistry score by 2 points.
(Note that the opportunity cost of a point on your economics exam is 2 points on your
chemistry exam, not 2 points on your chemistry exam plus 30 minutes of your time. The problem
says that you were going to spend the two hours studying. So if you didn’t spend the 30 minutes
studying for the economics exam, you would spend it studying for the chemistry exam. Thus, if you
decide not to spend the 30 minutes studying for economics, you would get another 2 points on your
chemistry exam; you wouldn’t get the 2 points plus 30 minutes of free time.)
b. The opportunity cost is $250. If you sell the Tickle Me Elmo on eBay, you have $250 more than
you would have if you gave it to your child. (It’s true that you would only have $225 more than you
had before you bought the doll to start with. But regardless of whether you give the doll to your
child, the $25 is already gone. The difference between what you have if you sell the doll and what
you have if you give it to your child is $250, so that’s what you’d be giving up by giving the doll to
your child.)
c. No. Regardless of whether you went to graduate school or took a job, you would have living
expenses. Thus, they aren’t part of the cost of going to graduate school. On the other hand, if you
didn’t go to graduate school, you wouldn’t have to pay tuition and you’d earn a salary. Thus both
tuition and the foregone salary are parts of the cost of going to graduate school.
2.a. The PPC for civilian and military goods and
services shows the various combinations of these two
types of output that the economy can produce using
exactly all of the available resources. This PPC for
civilian and military output probably has the
conventional bowed-out shape. Some labor and
capital are well suited to the production of civilian
goods and services, while other labor and capital are
well suited to the production of military goods and
services. Therefore, the opportunity cost of producing
either of these types of output rises as we produce
more of it.
Military
PPC
Civilian
The point where the PPC intersects the vertical axis is the point on the PPC where civilian
output is zero. Thus, it shows the amount of military goods and services we could get if we devoted
all of our resources to producing military output and none to civilian output. Similarly, the point
where the PPC intersects the horizontal axis shows the amount of civilian goods and services we
could get if we devoted all of our resources to producing civilian output. The slope of the PPC at a
given point shows the amount that military output would fall by if we increased civilian output by 1
unit. Thus, the slope is (minus) the opportunity cost of civilian goods.
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b. If there is no change in the productivity of capital
and labor in producing civilian goods and services,
then the maximum amount of civilian output we can
produce doesn’t change. Thus the point where the
PPC intersects the horizontal axis doesn’t change.
But since capital and labor are more productive in
producing military goods and services than before, if
we devote some of our capital and labor to the
military sector, we get more military output than
before. Thus at any point except where the PPC
intersects the horizontal axis, the new PPC is above
the old PPC. That is, the PPC shifts outward
asymmetrically—from something like PPC1 to
something like PPC2.
c. The problem focuses on a change in the
composition of production, not on the level of
production. This means that it describes a movement
along the PPC. Since a decision to spend more on
military goods and services doesn’t change the
economy’s productive possibilities, it can’t move us to
a point outside the old PPC. Given our productive
capacities, with the economy starting at full
employment (so that we’re already on the PPC), the
only way we can have more military goods and
services is by having fewer civilian goods and
services. Thus the change would move us from one
point on the PPC (such as point A) to another point
(such as point B) with more military output and less
civilian output.
Military
PPC2
PPC1
Civilian
Military
• B
• A
PPC
Civilian
3.a. The opportunity cost of a croissant for a worker is the number of baguettes he or she could
produce in the time it takes to produce 1 croissant. Since Juliette could produce 3 croissants in an
hour or 3 baguettes, her opportunity cost of 1 croissant is 1 baguette. Likewise, her opportunity cost
of 1 baguette is 1 croissant. The opportunity costs for each of the workers are given in the table
below.
Opportunity Cost
of 1 Croissant
(in Baguettes)
Juliette
Marie
Pierre
1
4
⅓
Opportunity Cost
of 1 Baguette
(in Croissants)
1
¼
3
b. When there is no specialization, we think of each worker splitting his or her time in the same
way as the others. That is, if one worker produces croissants for 1 hour and baguettes for 5 hours,
the other two workers also produce croissants for 1 hour and baguettes for 5 hours. We don’t allow
one worker to spend more time on some activity than another worker. Since the workers always do
the same thing, there’s a constant opportunity cost for the collective. Every time the three workers
work an hour producing baguettes, they produce 8 baguettes. Every time the three workers work an
hour producing croissants, they produce 7 croissants. Therefore, for the collective as a whole, when
there is no specialization, the opportunity cost of 1 croissant is ⁸⁄⁷ baguettes.
3
The vertical intercept of the PPC shows the
number of baguettes the three workers could produce
Baguettes
in a day if they produced no croissants. Since they
48
work for 6 hours per day and produce 8 baguettes
per hour, they could produce 48 baguettes. The slope
of the PPC is minus the opportunity cost of the good
PPC without
on the horizontal axis. Therefore, if we put croissants
specialization
on the horizontal axis, the slope of the PPC for the
collective, assuming no specialization, is –⁸⁄⁷.
Therefore, the PPC for the collective with no
specialization is a line starting at 48 baguettes and 0
croissants, with a slope of –⁸⁄⁷. The horizontal
Croissants 42
intercept shows the number of croissants the three
workers could produce if they produced no baguettes.
If the collective produced no baguettes, it could
produce 42 croissants (7 croissants per hour times 6 hours). Notice that this is the point we get to if
we start at no croissants and 48 baguettes and draw a line with a slope of –⁸⁄⁷ until we get to the
horizontal axis.
The PPC for the collective without specialization is a straight line because the opportunity cost
of a croissant doesn’t rise as more are produced. This is true because each worker’s abilities are
constant and we are forcing the three workers to always split their time in the same way. Therefore,
every time they produce one more croissant, they give up ⁸⁄⁷ baguettes.
c. When we allow the workers in the collective to specialize, they will no longer split their time in
exactly the same way. Instead, they will divide the activities according to comparative advantage.
This means that as we think about producing progressively more of one of the goods, the worker
with the lowest opportunity cost produces first, the second lowest next, and the highest last. If the
collective decides to have the workers specialize according to who has the lower opportunity cost, it
will use Pierre to produce croissants first, then Juliette, and then Marie.
The specialization will cause the slope of the PPC to change as we move along it. Between 0
croissants and the maximum amount that Pierre can produce in a day (which is 18 croissants), the
relevant opportunity cost is Pierre’s—he is the one switching between baguette production and
croissant production; Juliette and Marie are just making baguettes. Therefore, the slope of the PPC
is –⅓ in this range. Between 18 croissants and 36 croissants, which is the maximum amount Pierre
and Juliette can produce together, the relevant opportunity cost is Juliette’s—she is the one who is
switching between the two activities; Marie is just producing baguettes and Pierre is just producing
croissants. Therefore, the slope of the PPC is –1 in this range. Finally, between 36 croissants and 42
croissants, which is the maximum number of croissants the three can produce if they all just
produce croissants, the relevant opportunity cost is Marie’s—she is the one switching between the
two activities. Therefore, the slope of the PPC is –4 in this range. The vertical intercept of the PPC is
48 baguettes—the total number of baguettes the three workers can produce if they each spend all 6
hours making baguettes. The horizontal intercept is 42 croissants—the total number of croissants
the three workers can produce if they each spend all 6 hours making croissants.
4
With specialization, the PPC of the collective
has two kinks in it. This reflects the fact that with
specialization, the opportunity cost rises as the
collective produces more of a good. The slope of the
PPC changes from –⅓ (Pierre’s opportunity cost) for
the first segment, to –1 (Juliette’s opportunity cost)
for the second, and finally to –4 (Marie’s opportunity
cost) for the third. This happens simply because the
collective uses the worker with the lowest
opportunity cost first, the next lowest opportunity
cost second, and so on. As we add more and more
workers, the PPC would start to take on its
characteristic curved shape.
Baguettes
48
42
PPC with
specialization
24
18
36 42
Croissants
The quantities of croissants and baguettes at each kink point are calculated by thinking about
how much the workers can produce. The first kink occurs at the point where Pierre is producing
croissants full time and Juliette and Marie are producing baguettes full time. When Pierre is
spending 6 hours producing croissants, he will make 18 croissants; when Juliette and Marie are
producing baguettes full time, they will make 42 baguettes (18 from Juliette and 24 from Marie).
The second kink point occurs at the point where Pierre and Juliette are both producing croissants
full time and Marie is making baguettes full time. If Pierre and Juliette work 6 hours producing
croissants, they will make 36 croissants (18 from Pierre and 18 from Juliette); when Marie is
producing baguettes for 6 hours, she will make 24 baguettes.
4.a. As in lecture, for Robinson the opportunity cost of 1 coconut is 1 fish, and for Friday the
opportunity cost of 1 coconut is 4 fish. And as in lecture, if Robinson and Friday both spend all
their time fishing, they will catch 54 fish (6 from Robinson and 48 from Friday), and if they
spend all their time gathering coconuts they will get 18 coconuts (6 from Robinson and 12 from
Friday).
However, what happens between the two
extremes is different than in lecture. Starting from
the point where they are both spending all day
catching fish, suppose they decide to gather some
coconuts. The rule is that Friday must be the first one
to do this. For each coconut he gathers, he catches 4
fewer fish. Thus the slope of their production
possibilities over this range is −4. Robinson isn’t
allowed to gather any coconuts until Friday is
spending all his time doing so. Thus the slope is −4
up to the point where Robinson is still spending all
his time fishing, but Friday is spending all his time
gathering coconuts. At this point, they’re getting 6
fish and 12 coconuts. Beyond that point, if they want
more coconuts, it’s Robinson who switches from
fishing to coconut-gathering. Thus over that range,
the slope is determined by Robinson’s opportunity
cost, and so is −1.
Fish
54
6
12
18
Coconuts
5
The reason that Robinson and Friday’s production possibilities when they follow the rule has
this strange shape is that the rule makes them specialize according to comparative disadvantage:
the rule requires that if only one of them is gathering coconuts, it’s Friday, who has the higher
opportunity cost of gathering coconuts, and that if only one of them is fishing, it’s Robinson, who
has the highest opportunity cost of catching fish. Thus their production possibilities when they
follow the rule are worse than if they didn’t specialize at all but just divided their time the same
way.
b. When Robinson can catch 4 fish in an hour, he and Friday have the same opportunity costs: the
opportunity cost for either one of gathering a coconut is 4 fish. (For Robinson, it would take him an
hour to gather a coconut, and in that time he could have caught 4 fish. For Friday, it would take him
half an hour to gather a coconut, and in that time he could also have caught 4 fish.) Likewise, the
opportunity cost for either one of a fish is ¼ coconut. So, regardless of whether they trade off
between fish and coconuts by having Robinson gather coconuts, or by having Friday do it, or by
both switching some of their time from fishing to coconut-gathering, for each additional coconut
they gather, they catch 4 fewer fish. Thus, there are no gains from specialization.
The diagram shows this graphically. If both
Robinson and Friday spend all their time fishing,
they will catch 72 fish in a day. If the both spend all
their time gathering coconuts, they will gather 18. In
between, regardless of who specializes in what (or
whether they specialize at all), for each extra coconut
they gather, they catch 4 fewer fish. Thus either with
or without specialization, the PPC is a straight line
between the two extremes.
Fish
72
PPC with or
without
specialization
18
Coconuts
5.a. The information that limes have important
health benefits will mean that at a given price,
American consumers want to buy more limes. This
corresponds to a shift out in the demand curve (from
D1 to D2). The equilibrium price and quantity of limes
will both rise (from P1 to P2 and from Q1 to Q2,
respectively).
P
S1
P2
P1
D2
D1
Q
Q1 Q2
b. Limes and avocados are complements: they are
often consumed together. To put it another way,
consuming more avocados makes consuming limes
more attractive, and consuming fewer avocados
makes consuming limes less attractive. When the
price of avocadoes rises because of a shift in supply,
consumers buy fewer of them. As a result, consumers
seeking to make themselves as well off as possible
find that they can have more total happiness if they
P
S1
P1
P2
D2 D1
Q2 Q1
Q
6
also buy fewer limes (and buy more of goods whose enjoyment isn’t linked to their consumption of
avocados—salsa, for example). As a result, at a given price of limes, fewer will be demanded than
before. This corresponds to a shift back in the demand curve (from D1 to D2). The equilibrium price
and quantity of limes will both fall (from P1 to P2 and from Q1 to Q2, respectively).
c. Before the imposition of the price ceiling, the
equilibrium price of limes was P1 and the equilibrium
quantity was Q1. The statement that the price ceiling
is binding means that it’s less than the price where
supply and demand intersect—that is, that it’s below
P1. At the price ceiling of �
P, the quantity supplied (QS)
is less than the quantity demanded (QD). The price of
�), and the quantity bought
limes will fall (from P1 to P
and sold will fall (from Q1 to QS). Because the
quantity demanded will exceed the quantity supplied
at the new price, there will be a shortage of limes.
P
S1
P1
�
P
D1
QS Q1 QD
Q
Shortage
d. A tax that is paid by consumers shifts the demand
P
curve down by the amount of the tax: consumers are
willing to pay less at a given quantity because they
S1
know they will also have to pay the tax. Because the
P2 + tax
tax is paid by consumers, the supply curve isn’t
P1
affected. The downward shift of the demand curve
P2
lowers the equilibrium quantity (from Q1 to Q2). In
D1
addition, the equilibrium price, which is what firms
Tax (25¢)
receive, also falls (from P1 to P2). The price paid by
D2
consumers was P1, but after the tax is imposed the
Q2 Q1
Q
total amount they pay for each lime is P2 plus the tax.
Since the distance between D1 and D2 is the amount
of the tax, we find this amount paid by consumers by looking at the point on D1 corresponding to
the new equilibrium quantity (Q2). With a normal, downward-sloping demand curve and a
normal, upward-sloping supply curve, the tax decreases the amount suppliers receive for the good
and increases the amount that consumers pay.
6.a. For most consumers, there are many close substitutes for pepperoni pizza. Most obviously,
there are other types of pizza; but there are also meatball subs, burgers, calzones, and so on. With
the presence of many close substitutes, one would expect a small price increase to lead to a large
reduction in the quantity of pepperoni pizza demanded, and a small price decrease to lead to a large
increase in the quantity demanded. If so, the price elasticity of demand is fairly high.
(Of course, one could try to make an argument for a low elasticity. There are some consumers
who strongly prefer pepperoni pizza to any of the usual alternatives. The quantity of pepperoni
pizza that these consumers demand may be relatively unresponsive to the price. If these consumers
are the source of most of the demand for pepperoni pizza, the elasticity of demand is fairly low.)
b. The shift up of the supply curve will lead to a fall in quantity and a rise in price as we move along
the demand curve. In part (a), we argued that the price elasticity of demand for pepperoni pizza is
probably fairly high. If the elasticity of demand is greater than 1, the percentage fall in the quantity
of pepperoni pizza will be larger than the percentage rise in the price. As a result, total spending on
pepperoni pizza (which is price times quantity) will fall.
7
All of this is shown is the diagram. When the
P
S2
price elasticity of demand is high then, over the
S1
relevant range, the demand curve is fairly flat. In this
case, when the supply curve shifts up, the percentage
P2
fall in quantity (the percentage change from Q1 to Q2)
is larger than the percentage rise in price (the
P1
percentage change from P1 to P2). Total spending is
D1
the product of price and quantity. Thus it is shown by
the shaded rectangles in the diagram. For example,
total spending before the shift in supply is given by
the rectangle with corners at the origin, Q1 on the
Q2
Q1
Q
horizontal axis, P1 on the vertical axis, and the
intersection of D1 and S1. This rectangle has width Q1 and height P1, and so its area is Q1 times P1,
which is total spending on pepperoni pizza. Total spending after the shift in supply is shown by the
rectangle with width Q2 and height P2. As the diagram shows, with a high price elasticity of
demand, total spending falls when supply shifts up.