The Australian National University
ECON8025: Semester One, 2023
Tutorial 1 Answers
Dr Damien S. Eldridge
26 February 2023
A Note on Sources
These questions do not originate with me. They have either been influenced
by, or directly drawn from, other sources.
Key Concepts
Scarcity, Feasibility, Budget Sets, Budget Constraints, Budget Lines, Non-
Negativity Constraints, Time Constraints, Linear Prices, Non-Linear Prices,
Money Income Endowment, Commodity Bundle Endowment.
Tutorial Questions
Tutorial Question 1
Mr Smith consumes only two commodities. These are bread and water. In
1989, Mr Smith had an income of $100, while the prices of bread and water
were PB = $2 and PW = $1 respectively. The following year, in 1990, Mr
Smith’s income fell to $90, the price of bread fell to $1, and the price of water
remained unchanged at $1.
1. What is the equation for Mr Smith’s budget line in 1989?
2. What is Mr Smith’s budget set in 1989?
3. What is the equation for Mr Smith’s budget line in 1990?
1
4. What is Mr Smith’s budget set in 1990?
5. Illustrate Mr Smith’s 1989 and 1990 budget lines in a single diagram.
6. Are there any consumption bundles that are affordable in both years?
If so, identify them. Indicate where they lie in your diagram.
7. Are there any consumption bundles that are only just affordable in
both years (that is, that exhaust Mr Smith’s budget in both years)? If
so, find them. Indicate where they lie in your diagram.
8. Are there any consumption bundles that are affordable in 1989 but not
affordable in 1990? If so, identify them. Indicate where they lie in your
diagram.
9. Are there any consumption bundles that are affordable in 1990 but not
affordable in 1989? If so, identify them. Indicate where they lie in your
diagram.
10. Are there any consumption bundles that are unaffordable in 1989 and
also unaffordable in 1990? If so, identify them. Indicate where they lie
in your diagram.
Tutorial Question 2
Suppose that you have an income of $100 per week and can buy meat at a
price of $1 per kilogram.
1. Draw your budget constraint for bundles of meat and some composite
commodity known as “all other goods”, placing “quantity of meat” on
the horizontal axis.
2. Now suppose that your parents, in an attempt to deter you from becom-
ing a vegetarian, decide to subsidise your meat purchases by agreeing
to always pay one-half of your meat bill. Illustrate the impact this has
on your budget constraint.
3. Compare your new budget constraint with your old one.
Tutorial Question 3
On the planet Mungo, they have two kinds of money, blue money and red
money. Every commodity has two prices — a red-money price and a blue-
money price. Every Mungoan has two incomes — a red income and a blue
2
income. In order to buy an object, a Mungoan has to pay that object’s red-
money price in red money and its blue-money price in blue money. (The
shops simply have two cash registers, and you have to pay at both registers
to buy an object.) It is forbidden to trade one kind of money for the other,
and this prohibition is strictly enforced by Mungo’s ruthless and efficient
monetary police.
• There are just two consumer goods on Mungo, ambrosia and bubble
gum. All Mungoans prefer more of each good to less.
• The blue prices are 1 bcu (bcu stands for blue currency unit) per unit
of ambrosia and 1 bcu per unit of bubble gum.
• The red prices are 2 rcus (red currency units) per unit of ambrosia and
6 rcus per unit of bubble gum.
Answer the following questions.
1. Illustrate the red budget and the blue budget for a Mungoan named
Harold whose blue income is 10 and whose red income is 30. You might
like to use red ink for the red budget line and blue ink for the blue bud-
get line. Shade in the “budget set” containing all of the commodity
bundles that Harold can afford, given his two budget constraints. Re-
member, Harold has to have enough blue money and enough red money
to pay both the blue-money cost and the red-money cost of a bundle
of goods.
2. Another Mungoan, Gladys, faces the same prices that Harold faces and
has the same red income as Harold, but Gladys has a blue income of
20. Explain how it is that Gladys will not spend its entire blue income
no matter what her tastes may be.
3. Are Mungoan budgets really so fanciful? Can you think of situations on
earth where people must simultaneously satisfy more than one budget
constraint? Is money the only scarce resource that people use up when
consuming?
Tutorial Question 4
If the price of tomatoes rises from $2.00 per kilogram to $2.50 per kilogram,
while the price of apples rises from $1.00 per kilogram to $1.50 per kilogram,
in what sense has the price of tomatoes fallen?
3
Additional Practice Questions
Additional Practice Question 1
Dr Jones only consumes two commodities. These are books and sneakers.
Suppose that instead of being endowed with an exogenous money income, Dr
Jones is endowed with the commodity bundle that consists of six books and
two pairs of sneakers. You may interpret the market value of this commodity
bundle as Dr Jones’ implicit money income. But you should note that if either
or both of the commodity prices change, then the market value of Dr Jones’
endowment bundle, and hence his implicit income, will also change.
1. Suppose that the market price of books is $10 per book, while the
market price of sneakers is $5 per pair of sneakers. What is the market
value of Dr Jones’ endowment bundle (in dollars)?
2. Suppose that the market price of books is $8 per book, while the market
price of sneakers remains at $5 per pair of sneakers. What is the market
value of Dr Jones’ endowment bundle (in dollars)?
3. Illustrate the two different budget lines that you have found in a single
diagram.
4. How does the impact of the fall in the price of books, all else equal, in
this commodity endowment example differ from the one in which an
individual is endowed only with money income?
Additional Practice Question 2
Martha is preparing for exams in economics and sociology. She has time to
read 40 pages of economics and 30 pages of sociology. In the same amount
of time she could also read 30 pages of economics and 60 pages of sociology.
1. Assuming that the number of pages per hour that she can read of either
subject does not depend on how she allocates her time, how many pages
of sociology could she read if she decided to spend all of her time on
sociology and none on economics?
2. How many pages of economics could she read if she decided to spend
all of her time reading economics?
4
Answers for the Tutorial Questions
Answer for Tutorial Question 1
The situation in general
The equation for the budget line is
pBqB + pW qW = y,
which can be rearranged to obtain
qW = −
(
pB
pW
)
qB +
(
y
pW
)
.
The slope of this budget line in (qB, qW )–space is −
(
pB
pW
)
. (Note that the
graphical representation of (qB, qW )–space places qB on the horizontal axis
and qW on the vertical axis.) The largest amount of bread that Mr Smith
could afford to purchase is y
pB
. This would involve him spending all of his
money on bread, and nothing on water. Thus the the bread-axis intercept
bundle for Mr Smith’s budget line is
(
y
pB
, 0
)
. The largest amount of wa-
ter that Mr Smith could afford to purchase is y
pW
. This would involve him
spending all of his money on water, and nothing on bread. Thus the the
water-axis intercept bundle for Mr Smith’s budget line is
(
0, y
pW
)
.
Mr Smith is not required to spend all of his income, but is able to do so
if that is what he wants. Howevever, he cannot spend more than his income.
Furthermore, Mr Smith cannot purchase negative amounts of either bread or
water. This Mr Smith’s budget set is
B (pB, pW , y) = {(qB, qW ) : pBqB + pW qW 6 y, qB > 0, qW > 0} .
The situation in 1989
In 1989, the prices and income facing Mr Smith are (pB, pW , y) = ($2, $1, $100).
Thus the budget line facing Mr Smith is
2qB + qW = 100,
which can be rearranged to obtain
qW = −2qB + 100.
5
The slope of this budget line in (qB, qW )–space is −2, the bread-axis intercept
bundle for this budget line is (50, 0), and the water-axis intercept bundle for
this budget line is (0, 100). Mr Smith’s 1989 budget set is
B (pB = $2, pW = $1, y = $100)
= {(qB, qW ) : 2qB + qW 6 100, qB > 0, qW > 0} .
The situation in 1990
In 1990, the prices and income facing Mr Smith are (pB, pW , y) = ($1, $1, $90).
Thus the budget line facing Mr Smith is
qB + qW = 90,
which can be rearranged to obtain
qW = −qB + 90.
The slope of this budget line in (qB, qW )–space is −1, the bread-axis intercept
bundle for this budget line is (90, 0), and the water-axis intercept bundle for
this budget line is (0, 90). Mr Smith’s 1990 budget set is
B (pB = $1, pW = $1, y = $90)
= {(qB, qW ) : qB + qW 6 90, qB > 0, qW > 0} .
An illustration comparing 1989 and 1990
Since the slopes of the two budget lines are different, we know that they will
intersect each other precisely once. (If the slopes were the same, then they
would either be parallel lines, in which case they would never intersect, or
two copies of the same line, in which case they would intersect each other an
infinite number of times.) We can find their unique point of intersection as
follows. Note that
q1989W = q
1990
W ⇐⇒ −2qB + 100 = −qB + 90⇐⇒ 10 = qB ⇐⇒ qB = 10.
Upon substituting qB = 10 into the 1989 budget line, we obtain
qW = −2qB + 100 = −2(10) + 100 = −20 + 100 = 80.
As a check, note that if we had substituted qB = 10 into the 1990 budget
line, we would also have obtained
qW = −qB + 90 = −10 + 90 = 80.
6
Thus we can conclude that the unique point of intersection of the 1989 bud-
get line and the 1990 budget line occurs at the bundle (qB, qW ) = (10, 80).
The set of bundles that are affordable in both 1989 and 1990 is
A = {(qB, qW ) : 2qB + qW 6 100, qB + qW 6 90, qB > 0, qW > 0} .
This set is region A in the diagram below, including both of the budget line
boundaries.
The set of bundles that are not affordable in both 1989 and 1990 (that is,
neither affordable in 1989 nor in 1990) is
B = {(qB, qW ) : 2qB + qW > 100, qB + qW > 90, qB > 0, qW > 0} .
This set is region B in the diagram below, but excluding both of the budget
line boundaries.
The set of bundles that are affordable in 1989, but not affordable in 1990 is
C = {(qB, qW ) : 2qB + qW 6 100, qB + qW > 90, qB > 0, qW > 0} .
This set is region C in the diagram below, including the 1989 budget line
boundary but excluding the 1990 budget line boundary.
The set of bundles that are not affordable in 1989, but are affordable in
1990 is
D = {(qB, qW ) : 2qB + qW > 100, qB + qW 6 90, qB > 0, qW > 0} .
This set is region D in the diagram below, including the 1990 budget line
boundary but excluding the 1989 budget line boundary.
7
0 10
80
90
100
50 90
A
A
A
B
C
D
1989 Budget Line
1990 Budget Line
qB
qW
Answer for Tutorial Question 2
Let QM demote the quantity of meat (measured in kilograms), QC demote
the quantity of some composite consumption commodity, PM denote the
price of meat (measured in dollars per kilogram), PC denote the price of the
composite consumption commodity (measured in dollars per unit), and Y
denote your income (measured in dollars). Your budget constraint is the set
B (pM , pC , Y ) = {(QM , QC) : PMQM + PCQC 6 Y,QM > 0, QC > 0} .
The north-east frontier of this budget constraint in (QM , QC)-space is given
by the budget line
PMQM + PCQC = Y .
We will assume that the composite consumption commodity is the numeraire
in this situation. In other words, we will normalise the price of the composite
consumption commodity to be one dollar per unit (that is, we will set PC =
1). This allows us to interpret the quantity of the composite consumption
commodity that is purchased as “expenditure on all commodities other than
meat”, because
QC = ($1)QC = PCQC .
8
Upon doing this, the budget set becomes
B (pM , Y ) = {(QM , QC) : PMQM + QC 6 Y,QM > 0, QC > 0} ,
and the equation for the budget line becomes
PMQM + QC = Y .
Suppose that initially the price of meat is one dollar per kilogram (that is,
PM = 1) and your income is $100 (that is, Y = 100). In this situation, your
budget set is
B (1, 100) = {(QM , QC) : QM + QC 6 100, QM > 0, QC > 0} ,
and the equation for your budget line is
QM + QC = 100.
If your parents choose to pay for half of your expenditure on meat, then you
only need to pay for half of your total expenditure on meat. In this situation,
your budget line becomes
QM
2
+ QC = 100,
which can be rewritten as
(0.50)QM + QC = 100.
In effect, the generosity of your parents has halved the price of meat that
you face, moving it from one dollar per kilogram to fifty cents per kilogram.
Your new budget constraint is
B (0.50, 100) = {(QM , QC) : (0.50)QM + QC 6 100, QM > 0, QC > 0} .
Your budget sets before your parents provide their generous gift and after
your parents provide their generous gift are illustrated in the following dia-
gram. Before your parents generous gift, your budget constraint is given by
Area A in the diagram. After your parents generous gift, your budget con-
straint is given by the combination of Area A and Area B in the diagram.
9
QM (kg)
QC ($)
100
100
2000
Area A Area B
Answer for Tutorial Question 3
Part (1)
Harold faces two budget constraints: A red budget constraint and a blue
budget constraint. The equation for Harold’s red budget line is
2qA + 6qBG = 30⇐⇒ qA + 3qBG = 15⇐⇒ 3qBG = −qA + 15
⇐⇒ qBG = −
(
1
3
)
qA + 5.
The equation for Harold’s blue budget line is
qA + qBG = 10⇐⇒ qBG = −qA + 10.
The point of intersection of these two budget lines must satisfy the condition
that
qRBG = q
B
BG ⇐⇒ −
(
1
3
)
qA + 5 = −qA + 10⇐⇒
(
2
3
)
qA = 5
qA =
15
2
= 7.5.
10
Note that when qA = 7.5, we have
qRBG = −
(
1
3
)
(7.5) + 5 =
−7.5
3
+
15
3
=
7.5
3
=
15
6
=
5
2
= 2.5,
and
qBBG = −7.5 + 10 = 2.5.
Thus we can conclude that the point of intersection of Harold’s red budget
line and his blue budget line occurs at the commodity bundle (qA, qBG) =
(7.5, 2.5).
qA
qBG
0
CBS
CBS
CBS
CBS: Combined Budget Set.
10
10 15
5
7.5
2.5
Part (2)
Gladys also faces two budget constraints: A red budget constraint and a blue
budget constraint. The equation for Gladys’ red budget line is
2qA + 6qBG = 30⇐⇒ qA + 3qBG = 15⇐⇒ 3qBG = −qA + 15
⇐⇒ qBG = −
(
1
3
)
qA + 5.
The equation for Gladys’ blue budget line is
qA + qBG = 20⇐⇒ qBG = −qA + 20.
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The point of intersection of these two budget lines must satisfy the condition
that
qRBG = q
B
BG ⇐⇒ −
(
1
3
)
qA + 5 = −qA + 20⇐⇒
(
2
3
)
qA = 15
qA =
45
2
= 22.5.
Note that when qA = 22.5, we have
qRBG = −
(
1
3
)
(22.5) + 5 =
−22.5
3
+
15
3
=
−7.5
3
=
−15
6
=
−5
2
= −2.5,
and
qBBG = −22.5 + 20 = −2.5.
Thus we can conclude that the point of intersection of Gladys’ red budget
line and his blue budget line occurs at the commodity bundle (qA, qBG) =
(22.5,−2.5). Since the two budget lines have different slopes, we know that
this is their unique intersection point. Note that this bundle violates the non-
negativity restriction on qBG. This means that one of the budget lines must
lie strictly outside the other in the non-negative orthant of commodity-space
(non-negative quadrant in this two commodity case).
qA
qBG
0
CBS: Combined Budget Set.20
2015
5
CBS
12
Part (3)
The potential for multiple budget-like constraints to apply at once is very
realistic. In Britain during the Second World War, some commodities were
rationed by both price and other means. Suppose that the additional ra-
tioning device involved the use of coupons that were both limited in number
and transferable across commodities. In that case a person would face both
a regular monetary budget constraint and a coupon budget constraint. (I
do not know if this is in any way similar to the way that rationing actually
worked in Britain during the Second World War.) Even in regular times,
consumption typically requires time as well as money. As such, people face
both a monetary budget constraint and a time budget constraint.
Answer for Tutorial Question 4
The price of tomatoes has fallen relative to the price of apples. This can be
seen as follows:
p0T
p0A
=
2.00
1.00
= 2 > 1.67 ≈ 2.50
1.50
=
p1T
p1A
.
In other words, the price of tomatoes has fallen in real terms, because after
the price change a consumer would need to give up fewer apples to purchase
an additional tomato. The opportunity cost of tomatoes, on the market, has
fallen.
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Answers for the Additional Practice Questions
Answer for Additional Practice Question 1
Part (1)
The value of Dr Jones’ endowment bundle in this case is
pBωB + pSωS = ($10) (6) + ($5) (2) = $60 + $10 = $70.
In this case, the equation for his budget line is
pBqB + pSqS = pBωB + pSωS ⇐⇒ 10qB + 5qS = 70⇐⇒ 2qB + qS = 14.
Part (2)
The value of Dr Jones’ endowment bundle in this case is
pBωB + pSωS = ($8) (6) + ($5) (2) = $48 + $10 = $58.
In this case, the equation for his budget line is
pBqB + pSqS = pBωB + pSωS ⇐⇒ 8qB + 5qS = 58.
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Part (3)
qB
qS
0
7
14
7.25
11.6
6
2
Part (4)
Instead of the budget line rotating around the sneakers-axis intercept bundle
when the book price falls, it rotates through the endowment bundle. When
the endowment bundle contains positive amounts of both commodities, this
means that both the book axis intercept bundle and the sneakers-axis in-
tercept bundle will change when the book price falls. If books are on the
horizontal axis, then a fall in the price of books will result in a counter-
clockwise rotation through the relevant commodity bundle (sneakers-axis in-
tercept bundle for a money-income endowment, commodity endowment bun-
dle for a commodity bundle endowment). If books are on the vertical axis,
then a fall in the price of books will result in a clockwise rotation through
the relevant commodity bundle.
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Answer for Additional Practice Question 2
We are told that neither the number of pages of economics that Martha can
read per hour nor the number of pages of sociology that she can read per
hour depend on her allocation of time between the two activities. This means
that the time-price for a page of economics (tE) and the time-price for a page
of sociology (tS)are linear and can be treated as constant per-unit prices.
Assuming that Mary has some time-income, T , then her time-budget-line is
given by
tEqE + tSqS = T ,
where qE is the number of pages of economics that Mary reads and qS is the
number of pages of sociology that she reads. We are also told that the points
(q1E, q
1
S) = (40, 30) and (q
2
E, q
2
S) = (30, 60). Since we have two points that lie
on Martha’s time-budget-line, we can use the “two-point formula” (which is
hopefully familiar from high school) to find the equation for Martha’s time-
budget-line. Upon applying the two-point formula in this case, we obtain
qS − q1S
qE − q1E
=
q2S − q1S
q2E − q1E
⇐⇒ qS − 30
qE − 40 =
60− 30
30− 40 ⇐⇒
qS − 30
qE − 40 =
30
−10
⇐⇒ qS − 30
qE − 40 = −3⇐⇒ qS − 30 = −3 (qE − 40)⇐⇒ qS − 30 = −3qE + 120
⇐⇒ qS = −3qE + 150⇐⇒ 3qE + qS = 150.
Thus we can conclude that the equation for Martha’s time-budget-line is
3qE + qS = 150.
This means that tE = 3 hours per page of economics, tS = 1 hour per page
of sociology, and T = 150 hours. If Martha spends all of her time reading
economics, then she can read T
tE
= 150
3
= 50 pages of economics (and, of
course, no pages of sociology). If Martha spends all of her time reading
sociology, then she can read T
tS
= 150
1
= 150 pages of sociology (and, of
course, no pages of economics).
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