ECOS2001 – Intermediate Microeconomics
Tutorial 2- Answer Key
Chapter 4
Question 1
Joe’s utility function for movies at the theater (T) and DVDs watched at home (D) is given
by
2 24 d )n 2( 8 aT DU T D MU T MU D= + = =
1. Write an equation for MRSTD.
2. Would bundles of (T = 2 and D = 2) and (T = 1 and D = 4) be on the same indifference
curve?
3. Are Joe’s indifference curves convex? (Does MRSTD fall as T rises?)
Solution:
1. Using the equation for MRSTD, we find
DVD
theater
8 4
–
2
T
TD
D
Q MU T T
MRS
Q MU D D

= = = =

.
2. For bundles to lie on the same indifference curve, they must provide the same level of
utility.
For the first bundle: U(T = 2, D = 2) = 4(2)2 + (2)2 = 4(4) + 4 = 16 + 4 = 20.
For the second bundle: U(T = 1, D = 4) = 4(1)2 + (4)2 = 4(1) + 16 = 4 + 16 = 20.
Because the bundles provide the same level of utility, they must lie on the same
indifference curve.
3. To answer this question, calculate MRSTD at each of the bundles; remember
MRSTD = 4T/D.
When T = 1 and D = 4: MRSTD = 4T/D = 4(l)/4 = 1
When T = 2 and D = 2: MRSTD = 4T/D = 4(2)/2 = 4
So, Joe is willing to trade more DVD-watching for fewer theater tickets as he watches more
movies in the theater. What does this mean? Joe’s indifference curves are actually concave, not
convex, violating the fourth characteristic of indifference curves.
Question 2
James has $40 per week he can spend on movie tickets (M) at $10 each or burritos (B) at $5 each.
a. Write an equation for James’s budget constraint and draw it on a graph that has burritos
on the horizontal axis.
b. Suppose the price of burritos rises to $8. Draw James’s new budget constraint.
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Solution
a. The budget constraint represents bundles James can feasibly purchase, and takes the
form:
Income = PBB + PMM
40 = 5B + 10M
Since we are putting burritos on the horizontal axis, we want to find an equation for M
as a function of B, or
10M = 40 − 5B
M = 4 − 0.5B
b. To find the new budget constraint, simply change the price of burritos to $8.
Since the price of movie tickets has not changed, we know the budget constraint will
pivot inward, to a new horizontal intercept of 5 burritos.
Question 3
Sarah gets utility from soda (S) and hotdogs (H); her utility function is given by
= 0.50.5
Sarah’s income is $12, and the prices of sodas and hotdogs are $2 and $3, respectively.
What is Sarah’s utility-maximizing bundle of sodas and hotdogs?
Solution
The tangency condition for maximization is
S
H
S
H
MU P
MU P
= .
Substituting in the parameters yields
0.5 0.5
0.5 0.5
0.5 2
and
0.5 3
S SS
HH
MU S PHH
HMU S S P
−
−
= ==
.
So
2 2
or
3 3
H
H S
S
= = .
To find the exact quantities, use the budget constraint:
Income = PSS + PHH or 12 = 2S + 3H
S = 3 and H = 2
Question 4
Draw two indifference curves for each of the following pairs of goods. Put the quantity of the
1st good on the horizontal axis and the quantity of the 2nd good on the vertical axis.
a. Paul likes pencils and pens but does not care which he writes with.
b. Rhonda likes carrots and dislikes broccoli.
c. Emily likes hip-hop iTunes downloads and doesn’t care about heavy metal
downloads.
d. Michael only likes dress shirts and cufflinks in 1 to 1 proportions.
e. Carlene likes pizza and shoes.
f. Steven dislikes both fish and potatoes.
3
Solution
In the figures that follow, bundles along the indifference curve labeled U2 are strictly
preferred to bundles along the indifference curve U1.
a. Paul is equally as happy with a pen as with a pencil. Therefore, these two goods are
perfect substitutes.
b. Carrots are a good and broccoli is a bad for Rhonda.
c. Hip-hop is a good, heavy metal is a neutral.
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d. Dress shirts and cufflinks are perfect complements.
e. Both pizza and shoes are good for Carlene.
f. Steven’s indifference curves are downward-sloping; if you give Steven 1 more fish,
it will reduce his utility, so to keep his utility constant, you must increase his utility
by taking away some of the potatoes he dislikes.
Question 5
José gets satisfaction from both music and fireworks. José’s income is $240 per week. Music
costs $12 per CD, and fireworks cost $8 per bag.
a. Graph the budget constraint José faces, with music on the vertical axis and fireworks
on the horizontal axis.
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b. If José spends all his income on music, how much music can he afford? Plot a point
that illustrates this scenario.
c. If José spends all his income on fireworks, how many bags of fireworks can he
afford? Plot a point that illustrates this scenario.
d. If José spends half his income on fireworks and half his income on music, how
much of each can he afford? Plot a point that illustrates this scenario.
e. Connect the dots to create José’s budget constraint. What is the slope of the budget
constraint?
f. Divide the price of fireworks by the price of music. Have you seen this number
before and, if so, where?
g. Suppose that a holiday bonus temporarily raises José’s income to $360. Draw José’s
new budget constraint.
h. Indicate the new bundles of music and fireworks that are feasible, given José’s new
income.
Solution
José has income of $240,I = the price of music is $12,MP = and the price of fireworks is
$8.
F
P =
a.

b. 20
M
I
P
=
This is shown as the point labeled b in the figure below.
c. 30
F
I
P
=
This is shown as the point labeled c in the figure below.
d.
1
2 15
1
2 10
F
M
I
F
P
I
M
P
= =
= =
This is shown as the point labeled d in the figure below.
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e.
The slope of the budget constraint is
20 2
30 3
M
F

= − = −


f.
8 2
12 3
F
M
P
P
= =
This is –1 times the slope of the budget constraint.
g.
h.
The shaded area shows the new bundles of music and fireworks that are feasible for
Jose.
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Question 6
Find the utility-maximizing bundle for a Cobb Douglas utility function (, ) = 1−
where X and Y denote two goods and “a” is the preference parameter. Assume that and
denote the price of good X and Y, respectively, and I denotes the income.
Solution
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Question 7
Eric’s utility function is u(x, y) = 3x + 4y and faces prices px = $1 and py = $2.5 and income
I = $23. Comparing his MRSx;y and the price ratio, find his optimal consumption of goods x
and y. (Corner solution!)
Solution
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Question 8
John’s utility function is u(x, y) = 5 min{2x; 3y} and he faces prices px = $1 and py = $2 and
income I = $100. Find his optimal consumption of goods x and y.
Solution