Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 1 of 8
PROBLEM SET #1 Suggested Solutions
1. Supply and Demand
(2 points total; 1 point each) For each of the events described below, sketch a supply and demand graph that illustrates the
event. Be sure to properly label all curves and relevant points in your graph. In the area to the left of your graph, explain
why you think your graph is correct. In that area, also answer the questions asked.
a.
Spaghetti sauce sold in grocery stores: The economic recovery increases incomes of low and middle-income families.
What is the effect on the price of spaghetti sauce? On the quantity of spaghetti sauce sold?
For all supply/demand questions like this, we assume that all other things – aside from what is specified in the question –
stay the same (that is, we make the “ceteris paribus” assumption). Do not add events to the question that are not there.
Assume all other factors are held constant.
The question asks about the supply and demand for spaghetti sauce sold in grocery stores. The first step is drawing the initial
equilibrium (E) at P1 and Q1.
The second step: How do we capture the event? The event is an increase in income. To determine the effect of income on
spaghetti sauce sold in grocery stores, we first need to specify whether spaghetti sauce sold in grocery stores is a normal or
an inferior good. For a normal good, an increase in income results in an increase in demand. For an inferior good, an
increase in income results in a decrease in demand.
You could make either assumption – assume spaghetti sauce sold in grocery stores is a normal good OR assume spaghetti
sauce sold in grocery stores is an inferior good – but you have to make an explicit assumption. To make the assumption
“explicit” means communicating the assumption: writing it down. Had this been an exam question, you could not have
received full credit for your answer if you hadn’t explicitly recognized that the answer depended upon whether spaghetti
sauce sold in grocery stores is a normal or an inferior good.
If you assumed spaghetti sauce is a normal good, then the
increase in income causes an increase in the demand for
spaghetti sauce. Remember that the demand curve shows
how much of a good will be purchased at any given price.
At every possible price, there is more spaghetti sauce
demanded because of the increased income. When there is
an increase in demand, the demand curve shifts to the
right.
The third step: What is the effect on price and quantity?
The shift to the right of demand (that is, an increase in the
quantity demanded at every possible price), results in an
increase in the price and an increase in the quantity sold at
equilibrium.
The graph showing the market equilibrium before and
after the shift illustrates why this is the case. The demand
curve shifts to the right, changing the equilibrium point
from E1 to E2, increasing the equilibrium price from P1 to
P2, and increasing the equilibrium quantity from Q1 to
Q2. Note that the supply curve has not moved; it is only the
quantity supplied that rises.
If you assumed spaghetti sauce is an inferior good, then
the increase in income causes a decrease in the demand for
spaghetti sauce. Remember that the demand curve shows
how much of a good will be purchased at any given price.
At every possible price, there is less spaghetti sauce
demanded because of the increased income. When there is
a decrease in demand, the demand curve shifts to the left.
The third step: What is the effect on price and quantity?
The shift to the left of demand (that is, a decrease in the
quantity demanded at every possible price), results in a
decrease in the price and a decrease in the quantity sold at
equilibrium.
The graph showing the market equilibrium before and
after the shift illustrates why this is the case. The demand
curve shifts to the left, changing the equilibrium point from
E1 to E2, decreasing the equilibrium price from P1 to P2,
and decreasing the equilibrium quantity from Q1 to Q2.
Note that the supply curve has not moved; it is only the
quantity supplied that rises.
The graph is at the top right of the next page.
The graph is at the top left of the next page.
Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 2 of 8
For news stories related to this question, you can google “pasta sauce recession.” This article implies sauce is an inferior
good: http://online.wsj.com/news/articles/SB10000872396390444900304577579071446652942; this one implies sauce is a
normal good: http://www.chicagotribune.com/business/chi-sat-trading-downjan24-story.html
b.
Fresh fruit: Drought and the effects of climate change decrease the fruit harvest. At the same time, a successful antiobesity campaign encourages people to increase their consumption of fresh fruit. What is the effect on the price of fresh
fruit? On the quantity of fruit sold?
The question asks about the supply and demand for fresh
fruit. The first step is drawing the initial equilibrium (E1)
at P1 and Q1.
The second step: how do we capture the event? Notice
that there are two events in this question. Other than
these two specified events, we assume all else is constant.
That is, we invoke the ceteris paribus assumption.
Drought and the effects of climate change decrease the
fruit harvest. This is a decrease in the productivity of
land – one of the factors that shift the supply curve.
There is a decrease in the supply of fresh fruit. At every
possible price of fresh fruit, there is less fresh fruit
offered for sale due to the decreased harvest. The
quantity supplied decreases at each and every possible
price. The entire supply curve shifts to the left.
At the same time, a successful anti-obesity campaign encourages people to increase their consumption of fresh fruit. A
successful campaign generates a change in preferences, one of the factors that shift demand. The quantity demanded of fresh
fruit will increase at every price. There is an increase in the demand for fresh fruit which is shown by shifting the demand
curve to the right.
The third step: what is the effect on price and quantity? The shift to the left of supply (that is, a decrease in the quantity
supplied at every possible price), results in an increase in the price and a decrease in the quantity sold at equilibrium. The
shift to the right of demand (an increase in the quantity demanded at every possible price), results in an increase in price and
an increase in the quantity sold.
Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 3 of 8
So drought puts downward pressure on the
quantity but the anti-obesity campaign puts
upward pressure on the quantity. What is the
net effect on quantity? It depends. (You’ll
find “it depends” is often the answer in
economics. It’s never a sufficient answer,
though. We need to know on what “it
depends.”)
The net effect on quantity depends on which
shift is larger: the increase in demand or the
decrease in supply. If you drew the shifts the
same size, then you had no effect on quantity.
If you shifted demand more than you shifted
supply, quantity Q2 is more than quantity Q1.
If you shifted supply more than you shifted
demand, Q2 is less than Q1.
The three graphs illustrates why this is the
case. The supply curve shifts to the left and
the demand curve shifts to the right changing
the equilibrium point from E1 to E2. In all
cases, equilibrium price decreases from P1 to
P2. The effect on quantity depends upon
which curve shifts more: neither (quantity
unchanged), demand (quantity rises), or supply
(quantity falls).
2.
(4 points total) Production Possibilities
Frontier, Growth, and Gains from
Trade
Suppose the data describe the current
production possibilities for an economy that
produces two goods: household goods and
infrastructure (roads, bridges, communications
networks, and so on). Producing more
infrastructure could improve productivity a lot in the household goods sector and a little in the infrastructure sector. But
producing more household goods has no effect on productivity in either sector.
Quantities that can be produced per month with the currently available resources
household goods
infrastructure
Label point
a.
0
100
A
100
90
B
200
75
C
(½ point) Does this economy exhibit increasing opportunity costs?
300
50
D
Yes
350
30
E
No
400
0
F
(Circle one)
Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 4 of 8
Yes, this economy exhibits increasing opportunity costs. Increasing household goods production from 100 to 200 units (from
B to C) requires decreasing infrastructure production from 90 to 75 units, a drop of 15 units of infrastructure. But increasing
household goods production by another 100 units (from 200 to 300, from C to D) requires decreasing infrastructure
production from 75 to 50 units, a drop of 25 units of infrastructure. For a constant increase in household goods, there is an
ever-increasing cost in terms of the amount of infrastructure that cannot be produced with the available resources.
B. (½ point) Plot the PPF. Put infrastructure on
the vertical axis; household goods on the
horizontal axis. Label the points. Be sure each
axis is to scale (for instance, if 100 = ½", don’t
also let 100 = 1/4" or 3/4" along the same axis).
c. (1 point) Suppose the economy wanted to
consume 300 units of household goods and 80
units of infrastructure per month (label it G).
What is a combination of output chosen from A F that would quickly move the economy to G?
Explain your answer.
The more infrastructure the economy produces,
the faster it will grow. So combinations A, B, C
are going to produce faster growth than
combinations D, E, F.
The question underscores the importance of reading the question prompt carefully. The key sentences for this part are
highlighted above in yellow: Producing more infrastructure could improve productivity a lot in the household goods sector
and a little in the infrastructure sector. But producing more household goods has no effect on productivity in either sector.
That is: producing more roads, bridges, and so on makes it possible to produce a lot more household goods with the same
quantity of resources (capital, land and labor) than was possible with fewer roads, bridges, and so on.
This is an example of asymmetric growth. The
increased production of infrastructure benefits the
household goods sector more than it benefits the
infrastructure sector. Roads and bridges make it
possible to transport inputs to the production process
and finished goods more cheaply (faster, and at lower
cost), increasing productivity in the household goods
sector a lot. But more roads and bridges have only a
small effect on the efficiency of production of yet more
roads and bridges, which is why productivity in the
infrastructure sector improves only a little.
When more infrastructure is produced, there is a big
increase in productivity in the household goods sector
and a small increase in productivity in the
infrastructure sector. The maximum amount of
infrastructure the economy could produce if all
resources were devoted to infrastructure production
increases a little bit. That means the end point on the vertical axis moves up a little. The maximum amount of household
goods the economy could produce if all resources were devoted to household good production increases a lot. That means
the end point on the horizontal axis moves a lot to the right.
We don’t know the exact effect on productivity so we just sketch in a new production possibilities frontier. It will have an
endpoint a bit higher on the vertical (infrastructure) axis and a lot further out on the horizontal (household goods) axis.
Department of Economics
University of California, Berkeley
Problem Set #1
d.
Fall 2014
Economics 1
Page 5 of 8
(1 point) Again suppose the economy wanted to consume 300 units of household goods and 80 units of infrastructure per
month (label it G). The economy is currently at point C. Calculate the economy’s opportunity cost (OC) of increasing
production of household goods. This economy decides it wants to trade, purchasing household goods. What can you say
about a potential trading partner’s opportunity cost of producing household goods? Explain your answer.
The economy is at C, producing 200 household goods and 75 units of infrastructure. If the economy increases production of
household goods it will move toward point D. An increase of 100 units of household goods “costs” 75-50 = 25 units of
infrastructure. That’s the opportunity cost of 100 more units of household goods. Divide by 100 to get the opportunity cost
of 1 more unit of household goods: 25/100 = 0.25. When moving from C to D, each additional unit of household goods has
an opportunity cost of 0.25 units of infrastructure.
If the economy decides it wants to trade for household goods, it only makes sense to trade with an economy that has a lower
opportunity cost of producing household goods. So any potential trading partner’s opportunity cost of increasing household
goods must be less than 0.25 units of infrastructure.
e. (1 point) Bridges to Prosperity arrives in this
economy and builds bridges as described in the
reader. Draw a PPF below that illustrates the effect
of the work of Bridges to Prosperity on this
economy. On the right, explain why you drew
your graph the way you did.
Bridges to Prosperity (B2P) builds bridges with
local materials and labor, but with donated
expertise. This is an example of aid provided to a
country, which allows consumption of a
combination of output outside of the PPF.
There is no shift of the PPF. The available
resources have not increased. The productivity has
not increased. Instead this is an example of how
aid (a gift from outside the economy) increases the
consumption possibilities beyond what an economy
can produce.
If the economy wants to consume 300 units of household goods and 80 units of infrastructure – a combination beyond its
PPF – this could be accomplished with aid. If B2P provides 30 units of infrastructure, then the economy only needs to
produce 50 units of infrastructure. That will provide a total of 80units of infrastructure: 30 from aid + 50 from domestic
production. The remaining resources can be allocated to the production of household goods. Using the table in the
question’s prompt we see that if the economy is producing 50 units of infrastructure, it can use the rest of its resources to
produce 300 units of household goods.
3. Effect of a tax
(2 points total) About 15 billion gallons of soda (equivalent to 120 billion 16-oz bottles of soda) are sold in the U.S. each
year – about 45 gallons of soda per year for each man, woman, and child in the U.S. At about 1,500 calories per gallon, is it
any wonder we have an obesity epidemic? One proposal for fighting obesity by lowering soda consumption is to implement
a soda tax of 1¢ per ounce. So a typical 16 oz. bottle of Coke would have a 16¢ tax added to it. The tax would be collected
by the seller who would remit it to the government.
a.
(½ point) Suppose the graph at the right depicts the market for 16 oz. bottles of soda before the tax increase. On the
graph, show the effect of the additional 1¢/ounce tax. What is the new equilibrium price paid per 16 oz. bottle and new
equilibrium quantity of 16 oz. bottles of soda consumed?
Department of Economics
University of California, Berkeley
Problem Set #1
New price = about $1.55 per bottle
Fall 2014
Economics 1
Page 6 of 8
New quantity = about 113 billion bottles of soda per year
The tax can be thought of as an increase in the cost
of producing bottled soda. The tax increases the cost
of selling a single bottle by 16 cents. Hence, the
graph shows a second supply curve S2 that is
$0.16 higher than the previous supply curve S0 at
any quantity of bottled soda sold. This is the same
as an inward, or leftward, shift of the supply curve.
Note that the suppliers do not keep the additional
$0.16 per bottle; they immediately remit the $0.16 to
the government. The producers will retain the
price consumers pay, minus $0.16, per bottled soda.
The initial equilibrium at point A is at a price of
$1.50 per bottled soda and quantity sold of 120
billion bottled soda sold per year. The new
equilibrium point occurs at point B, where S2 crosses
the demand curve, D. Looking at the graph, this
point is located where the price paid per bottled
soda is about $1.55 and the quantity sold is
approximately 113 million bottled sodas per year. The drop in quantity demanded is due to the higher price: $1.55 > $1.50.
You aren’t expected to do the math to solve for the exact new equilibrium, but if you did . . . you probably used the pointslope formula to come up with an equation for the demand curve and a separate equation for the supply curve. Then the next
step was to solve this system of two equations with two unknowns. The precise results are p = 1.5533 and q = 113.33. Again,
listen up, you were not expected to solve for the exact new equilibrium, just to look at your graph and estimate p & q.
b.
(½ point) On your graph, use shading
to depict the old and new amounts of
consumer surplus, and the old and new
amounts of producer surplus.
It would have been better if the graph had
continued all the way to a quantity of 0
rather than being cut off at 100. The ideas
behind the shading are all the same, but the
shading should continue all the way to
quantity of 0. If you caught that, bravo! If
you didn’t, no worries. What matters is that
you get the basic ideas for consumer &
producer surplus.
Consumer surplus is the “I got a deal!”
feeling that consumers have when they pay
a price that is less than the maximum they
are willing to pay. Economists put a dollar
value on that consumer surplus. If I pay
$1.50 for something I was willing to pay
$1.65 for, I receive $0.15 (15 cents) of consumer surplus.
Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 7 of 8
On a graph, the consumer surplus for the economy as a whole is the area below the demand curve and above the price.
(Calculus geeks are thinking “Oh, cool, integration.” Yes, in Econ 100A and 101A. For now, just a shaded area on a
graph.) The original CS is the yellow triangle below the demand curve and above the price $1.50.
Once the price increases, consumer surplus declines. Some people are no longer buying the item because the maximum price
they were willing to pay is less than $1.55, and so they are receiving no CS whatsoever from bottled soda. The others are all
now paying a higher price: $1.55 instead of the original price of $1.50. Their willingness to pay hasn’t changed; the
demand curve hasn’t shifted. If I now pay $1.55 for something I was willing to pay $1.65 for, I receive $0.10 (10 cents) of
consumer surplus. So those buyers who were willing to pay at least $1.55 are still buying soda, but are receiving less
consumer surplus when they do so.
On a graph, the new consumer surplus is the light yellow triangle with vertical hash marks: a triangle below the demand
curve and above the new price, $1.55.
Producer surplus is the “I made a killing!” feeling that seller get when they sell something at a price that is above the
minimum they were willing to accept. Economists put a dollar value on that producer surplus. If someone pays $1.50 for
something that a seller had been willing to sell for $1.30, the seller receives $0.20 (20 cents) of producer surplus.
The original producer surplus is the area above the original supply curve and below the original price of $1.50. That’s the
purple shaded area in the graph.
Once the tax is implemented, the price paid by
consumers goes up, but the amount retained by the
sellers goes down. The sellers now have to send
164 to the government for every bottle of soda
sold. So from the sellers perspective, the price
retained is the new price ($1.55) minus the tax
($0.16), or $1.39. The producer surplus declines.
Some sellers are no longer selling soda because
$1.39 is less than they are willing to sell soda for.
Other sellers are still selling because they are
willing to sell so long as they can retain at least
$1.39. But on each bottle, they are receiving 11
cents less than they did before the tax. Their
producer surplus has declined.
On a graph, the new producer surplus is the light
purple triangle with vertical hash marks: a
triangle above the supply curve and below the new
price.
And here comes geometry and congruent triangles back to haunt you: The area of the light purple triangle in the graph is
the same as the area of the light blue triangle at right. Side-angle-side congruence. So you could have sketched in either
area: light purple (below $1.39 and above the original S curve) or light blue (below $1.55 and above the second S curve).
Congruent triangles = same area = same producer surplus.
c.
(1 point) Why did the price rise? Why did the price rise by less than the full amount of the tax?
The price rises because the costs of production – in the form of an excise tax – increased. Sellers are not willing to produce
the same quantity 120 billion bottles now that their costs are 16 cents higher.
The sellers may try to pass the entire tax on to their buyers, increasing price from $1.50 to $1.66. But they won’t be able to.
At a price of $1.66, sellers can’t sell as much soda as they could at a price of $1.50. That’s because buyers are not willing to
buy as much soda at a price of $1.66 as they were willing to buy at a price of $1.50. The demand curve slopes down. As the
Department of Economics
University of California, Berkeley
Problem Set #1
Fall 2014
Economics 1
Page 8 of 8
price increases above $1.50, quantity demanded falls. So the price rises, but not by the full 16 cents.
The only time buyers can pass on the entire tax is when the demand curve is vertical. The only time buyers can’t pass on any
of the tax is when the demand curve is horizontal. In any other case, the burden of the tax will be borne by both buyers and
sellers.
4. Essay: The Price Mechanism (2 points total)
Write a one-page essay in which you address these points:
$
Give an example of a good or service that is allocated to buyers using the price mechanism. Do not use an example that
was discussed in lecture; come up with a new example. Should society use the price mechanism to determine for whom
this good is produced? Why or why not?
$
Now give an example of a good or service that is currently not allocated to buyers using the price mechanism. Do not
use an example that was discussed in lecture; come up with a new example. What is the non-price rationing mechanism
that determines for whom this good or service is produced? Should society not use the price mechanism to determine for
whom this good is produced? Why or why not?
Of course, there are lots of specific examples, so we can’t provide you with “this is what you should have written.”
Guidelines:
a. Did you follow the specifications? Maximum 400 words? Maximum one page? 1” margins? Double-spaced? 10 or 11
or 12 pt font? Your name, date, and word count in the top right corner? Your essay stapled at the back of your problem set?
Attached your “works cited” list (either at the end of page 1 or on a separate page)?
If so, you remained eligible for full credit. If not, you lost a point right off the top.
b. Did you choose an example of a good or service that is allocated using the price mechanism? Did you then choose a
second example of a different good or service that is not allocated using the price mechanism? Did you describe the
rationing mechanism that is used to allocate this second good or service to consumers? If so, good!
For example, who gets to purchase a semester at Cal? Is that determined by price? No. If it was, then education would go
to the people willing and able to pay the most. Instead, we have an admissions process – a non-price rationing mechanism –
that determines who is going to purchase a semester at Cal and who is not. Even someone with the richest parents in the
world is not allowed to purchase a Cal education if they have 400 on their SATs and a 1.8 gpa in high school.
But who gets to purchase a Cal sweatshirt? Anyone who is willing and able to pay the market price. The price mechanism
determines who are the buyers of Cal sweatshirts.
c. When you answered the questions about whether or not society should use (or not use) the price mechanism for
allocating the goods you chose, did you recognize that this is a normative question? Did you remember that in order to
answer any normative question, you must first explicitly state what goal we are trying to achieve? Did you explicitly state a
goal, and then write up your analysis in light of that goal? If so, good!