ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
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Content for Today
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Opportunity cost
Production Possibility Frontiers
Math review (time permitting)
Questions
A) Opportunity cost questions:
1. Larry was accepted at three different universities, and must choose one.
Yale costs $50,000 per year and did not offer Larry any financial aid. Larry
values attending Yale at $60,000 per year. UW-Madison costs $30,000 per
year, and offered Larry an annual $10,000 scholarship. Larry values
attending UW-Madison at $40,000 per year. Edgewood College costs
$20,000 per year, and offered Larry a full $20,000 annual scholarship.
Larry values attending Edgewood at $15,000 per year. Which college
should Larry attend? What is his opportunity cost of attending this
college?
Answer: Larry’s net gain from attending Yale is (60,000 – 50,000) = $10,000 per
year. His gain from attending UW Madison is $20,000 per year and his gain from
attending Edgewood is $15,000 per year. Hence he should attend UW Madison
and his opportunity cost is the $15,000 surplus he would have made if he had
attended Edgewood instead.
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
2. Russell and Stephen are taxi drivers who are thinking about switching
careers. Russell rents his taxi, fully equipped, from someone else at a rate
of $75/day. Stephen owns his taxi so he does not have to pay rent.
Consider the following statement: “All else being equal, Stephen is more
likely to continue being a taxi driver since he does not have to pay the cost
of renting the taxi and so makes more profit than Russell.” Do you agree
with this? Why/why not?
Answer: I do not agree with this. While Stephen does not have to pay the rental
cost, he could rent the taxi to someone else: thus if he drives the taxi himself he
forgoes the $75/day in rent he could have earned, so he has an implicit cost of
forgone rent. Hence, all else being equal, Stephen and Russell face the same
incentives when making this decision.
B) Production Possibility Frontiers
1. Jack and Jill each own a farm, where they can each produce milk and
bread. In a given day, Jack and Jill can produce gallons of milk and loaves
of bread. The maximum amount of either good they can produce if they
produce none of the other is given by the following table:
Jack
Jill
Gallons of milk per day Loaves of bread per day
with no bread
with no milk
2
6
10
2
a. Draw the individual PPFs of Jack and Jill with milk on the x axis.
b. What is the opportunity cost of producing one more gallon of milk
for Jack? For Jill?
c. Describe who has the absolute advantage and who has the
comparative advantage in which goods.
d. Who should specialize in the production of milk if Jack and Jill
trade?
e. Can Jack and Jill each consume 5 gallons of milk and 3 loaves of
bread if they trade? What about if they did not trade?
f. (Extension – not assessable) Can you construct a PPF showing how
much Jack and Jill can product in total? Hint: first figure out how
much of each good they could make if they made none of the other
good. Then figure out who should make the first gallon of milk.
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
Answers:
b. To make 2 gallons of milk Jack gives up 6 loaves of bread. Hence to make one
gallon of milk Jack gives up 3 loaves of bread, so the opportunity cost of one
gallon of milk for jack is 3 loaves of bread. Similarly the opportunity cost of a
gallon of milk for Jill is 2/10 = 1/5 loaves of bread.
c. Jack has the absolute advantage in bread since he can make more bread in a
day than Jill. Jill has the absolute advantage in milk. Jill has the comparative
advantage in milk since her opportunity cost is lower than Jack’s (1/5 < 3). Jack
has the comparative advantage in bread (1/3 < 5 – note that the opportunity cost
of bread for a person is the reciprocal of the opportunity cost of milk).
d. Since Jill has the comparative advantage in milk she should specialize in milk
if the two of them trade.
e. If they trade, yes: Jack makes 6 loaves of bread and Jill makes 10 gallons of
milk and they each swap half their output. Without trade Jack cannot make 5
gallons of milk and Jill cannot make 3 loaves of bread, so this allocation can only
be achieved with trade.
f. The maximum amount of milk they can produce together, with no bread, is 12
gallons. With no milk they can produce 8 loaves of bread together. Now, if they
start by producing 8 loaves of bread and no milk and then decide to make a
gallon of milk, Jill should make the first gallon of milk, since she has the lower
opportunity cost (i.e. this costs the smallest number of loaves of bread). This is
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
true for any number of gallons of milk up until 10. At 10 gallons of milk Jack is
producing 6 loaves of bread and no milk, while Jill is producing no bread. Thus if
they want even more milk Jack has to switch from producing bread to milk, so
the slope of the joint PPF changes sharply. The diagram is below:
2. Crusoe finds himself stranded on an island. He devotes 10 hours each day
to either gathering coconuts or catching fish. Crusoe can gather 4 coconuts
in an hour, but he needs 5 hours to catch a single fish. On the other side of
the island is Friday. Friday also devotes 10 hours each day to gathering
coconuts and fishing. He can gather 3 coconuts per hour and needs only
2.5 hours to catch a fish.
a. Construct a table showing how much each person can produce of
each good if they do not produce any of the other good
b. What is the opportunity cost of catching a fish for Crusoe? For
Friday?
c. What is the opportunity cost of gathering a coconut for Crusoe? For
Friday?
d. Draw Crusoe’s production possibilities frontier with coconuts on
the x-axis. Give its equation (with the number of fish on the left
hand side). On a separate graph, do the same for Friday.
One day, Crusoe and Friday befriend each other and they decide to explore the
possibility of trade.
e. For maximum output, who should specialize in coconuts? In fish?
Justify your answer using the language of comparative advantage.
Who has the absolute advantage in each good?
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
Answers:
a. Here is the table:
Crusoe
Friday
Max coconuts with no fish
10*4 = 40
10*3 = 30
Max fish with no coconuts
10/5 = 2
10/2.5 = 4
b, c. Let’s also put the opportunity costs in a table:
Crusoe
Friday
Opportunity cost of a coconut
2/40 = 1/20 fish
4/30 = 2/15 fish
Opportunity cost of a fish
40/2 = 20 coconuts
30/4 = 15/2 coconuts
d.
Since we already know the slopes (they are the opportunity cost of coconuts –
made negative!) and the vertical intercepts we can read these of the graph:
Crusoe: Fish = 2 – (1/20) Coconuts
Friday: Fish = 4 – (1/15) Coconuts
e. Friday has the lower opportunity cost of fish, so he should specialize in fish as
his comparative advantage is in fish. Crusoe has the lower opportunity cost of
coconuts, so he should specialize in coconuts, as that is his comparative
advantage.
In this case since Crusoe can gather more coconuts than Friday and Friday can
gather more fish than Crusoe, Crusoe has the absolute advantage in coconuts
and Friday has the absolute advantage in fish.
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
C) Math Review Questions
We will use a fair amount of math this semester to illustrate important economic
concepts. Economics is a quantitative and analytical discipline, so the use of
mathematics is unavoidable. We will assume you are moderately comfortable
with the questions below: please take the time to make sure you can do them!
Math is a skill rather than a body of facts, so it is quite usual to find yourself a bit
“rusty” if you haven’t done algebra in a while.
1. Suppose a straight line passes through the points (0, 10) and (10, 20). Find
the equation of this line.
Answer: The slope is rise/run = (20-10)/(10-0) = 1. The y intercept is at y = 10, so
the equation is y = 10 + x. If you do not see this right away, write y = b + mx.
Since m = 1, you can substitute either point into y = b + x to find b.
2. Consider the following two equations, which are straight lines:
(I)𝑦 = 2𝑥
(II)𝑦 = −𝑥 + 15
a. Plot these two lines
b. Calculate the point where these two lines intersect. Label this point
A.
c. Consider shifting line (I) 3 units to the left. What is the equation of
this new line? Plot it on your diagram. Let’s call this line (I’).
d. Calculate where lines (I’) and (II) intersect. Label this point B.
e. Draw a vertical line (i.e. parallel to the Y axis) passing through B.
You will observe that this line and lines (I) and (II) form a triangle:
calculate the area of this triangle.
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
Answers:
a.
b. At A the y values of both lines are the same, so:
2𝑥 = −𝑥 + 15
3𝑥 = 15
𝑥=5
Substitute this into either equation to find y:
𝑦 = 2𝑥 = 2 × 5 = 10
c. Shifting lines horizontally often trips students up. It is tempting to write:
𝑦 = 2𝑥 + 3
However, this will shift the line vertically. That is, just adding three to the
equation will mean that for every x, y will now be 3 units higher. Instead we
want to change the equation so that for every y, x is 3 units less. The most
methodical method of doing this is to rearrange the equation to get x on the left
hand side, then shift the line, then rearrange again to get y on the left hand side.
𝑦 = 2𝑥
𝑦
𝑥=
2
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
Now shift the line to the left:
𝑦
𝑥 = −3
2
Rearrange to get x on the left hand side:
𝑦
𝑥+3=
2
𝑦 = 2(𝑥 + 3) = 2𝑥 + 6
If you are used to shifting lines horizontally you may skip this working and just
write 𝑦 = 2(𝑥 + 3), though this is the sort of question where I think a slightly
slower but more intuitive method is usually less error prone than just jumping to
the answer.
d. The working here is the same as in (b):
2𝑥 + 6 = −𝑥 + 15
3𝑥 = 9
𝑥=3
𝑦 = −3 + 15
= 12
e. The area of a triangle is, of course, just half times the base length multiplied by
the height of the triangle. We have one of the dimensions “for free” as the
difference between the x ordinate at A and B, i.e.
5– 3 = 2
To find the length of the other dimension of the triangle (which many people
refer to as the “base” but which I often call the “height”, since it is along the y
axis) we need the y ordinate of line (I) when x = 3:
𝑦 = 2×3= 6
Then the length is:
12 − 6 = 6
Therefore the area of the triangle is:
1
𝐴𝑟𝑒𝑎 = × 2 × 6 = 12 𝑢𝑛𝑖𝑡𝑠 2
2
3. Repeat the above question using these two equations:
(I)𝑦 = 4𝑥 + 6
(II)𝑦 = −2𝑥 + 60
Answers:
a. The diagram is similar to the one from the previous question, except the line
𝑦 = 4𝑥 + 6 has a y intercept above zero instead of passing through the origin (i.e.
the point (0,0)). Obviously many of the numbers will be different. For the rest of
the question working is the same as above.
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ECON 101: Principles of Microeconomics – Discussion Section Week 1 – Spring 2015
TA:
b. x = 9, y = 42
c.
𝑦 = 4𝑥 + 18
d. x = 7, y = 46
e. On I when x = 7, y = 34. Then the required area is:
1
𝐴𝑟𝑒𝑎 = × 2 × (46 − 34) = 12 𝑢𝑛𝑖𝑡𝑠 2
2
If you had any difficulty with the above, or if you feel like you could use more
practice,
a
good
collection
of
resources
can
be
found
at:
http://quiz.econ.usyd.edu.au/mathquiz/ (this page is from another university,
so ignore references to things like the “Math Learning Center”.
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