Name: ______Solutions____
Cosumnes River College
Principles of Microeconomics
Problem Set 5
Due Tuesday, March 10, 2015
Spring 2015
Prof. Dowell
Instructions: Write the answers clearly and concisely on these sheets in the spaces provided.
1. Fill in the blanks in the following table. The price of a cup of coffee is $2.
Cups of Coffee
TU
MU
MP/P
0
0
1
15
15
7.5
2
27
12
6
3
37
10
5
4
45
8
4
5
51
6
3
6
57
5
2.5
7
55
2
-0.5
8
50
-5
-2.5
2. State whether the consumer in each of the following situations is maximizing utility. If she is
not, state what adjustments she should make to maximize utility.
a. Selma consumes 2 sandwiches and 3 Coca-colas. The last sandwich gives Selma 25 units
of utility and the last Coca-cola gives her 5 units of utility. Sandwiches cost $5 apiece and
Coca-colas cost $1 apiece.
She is maximizing utility, since MUcoke/Pcoke = MUm&m/Pm&m.
b. Kristin eats 2 Twix bars and 1 bag of M&Ms. The last Twix bar gives Kristin 10 units of
utility and the last bag of M&Ms gives her 30 units of utility. Twix bars cost $0.50 apiece
and one bag of M&Ms costs $0.75.
She is not maximizing utility. The marginal utility per dollar of Twix (20) is less than the
marginal utility per dollar of M&Ms (40). She should eat more M&Ms and fewer Twix.
c. Jackie reads another chapter in her novel that gives her 400 units of utility at a cost of 30
minutes of her time and another chapter in her economics text that gives her 1,500 units of
utility at a cost of 1 ½ hours of her time.
She is not maximizing utility. The marginal utility per hour of reading economics (1000)
is more than the marginal utility per hour of reading romance novels (800). She should
read more economics and less romance.
Principles of Microeconomics: Problem Set 5
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3. The table below shows the total utility (TU) that Bubba receives from consumption of three
different goods (A, B, and C). Bubba’s weekly income is 42.00, and the prices of goods A, B,
and C are $1, $3 and $8 respectively.
Quantity
TUA
Good A
MUA
MUA/PA
TUB
Good B
MUB
MUB/PB TUC
Good C
MUC
MUC/PC
0
0
--
--
0
--
--
0
--
--
1
7
7
7
15
15
5
20
20
2.5
2
13
6
6
27
12
4
38
18
2.25
3
18
5
5
36
9
3
54
16
2
4
22
4
4
42
6
2
68
14
1.75
5
25
3
3
45
3
1
80
12
1.5
6
27
2
2
45
0
0
90
10
1.25
7
28
1
1
42
-3
-1
98
8
1
8
28
0
0
36
-6
-2
104
6
0.75
9
27
-1
-1
27
-9
-3
108
4
0.50
a. In the table, calculate and enter the marginal utility (MU) for each of the goods consumed.
b. Compute the marginal utility per dollar for each unit of each good consumed and enter the
results in the columns labeled MU/P.
c. Bubba does not get any pleasure out of saving money, so he will spend all of his earnings
each week. In order to maximize his overall utility, how many units of each good will he
consume?
Note that you are only looking for that combination for which the ratio of MU/P is the
same for all three goods that results in Bubba spending his entire income. This is:
6 units of good A
4 units of good B
3 units of good C
d. What is Bubba’s total utility?
TU = 27 + 42 + 54 = 123
e. What is the marginal utility per dollar from the last unit of each good consumed?
MU per dollar is 2
Principles of Microeconomics: Problem Set 5
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4. At a consumer optimum (point of utility maximization) involving goods A and B, the
marginal utility of good A is twice the marginal utility of good B. The price of good B is
$3.50. What is the price of good A?
We know the utility maximizing condition
MU A MU B
is satisfied. Substitute in the price

PA
PB
of good B, $3.5 and MU A  2MU B to get
2MU B MU B

. Divide both sides by MU B
PA
3.5
and cross multiply to get PA  2(3.5)  7 . Note that you may also solve this with simple logic.
If the last unit of good A yields twice the marginal utility of good B, then it’s price must be twice
that of good B.
5. After monitoring your daily consumption patterns, you determine that your daily consumption
of soft drinks is 3 and your daily consumption of tacos is 4 when prices per unit are $1 and $2
respectively. Explain what happens to your consumption bundle, the marginal utility of soft
drinks and the marginal utility of tacos when the price of soft drinks rises to $1.50.
With S representing soft drinks and T representing tacos, your original unity maximizing
MU S MU T

. After the increase in the price of soft drinks, you will have
PS
PT
MU S MU T

. Since you get more marginal utility per dollar spent on tacos than on
PS
PT
condition is
soft drinks, you will increase consumption of tacos and decrease consumption of soft drinks
until equality is restored. (Due to the law of diminishing marginal utility, the marginal utility of
tacos will decrease as consumption increases and the marginal utility of soft drinks will increase
as consumption decreases.)
Principles of Microeconomics: Problem Set 5
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6. Your monthly budget for entertainment is $48 and your entertainment goods are cable TV and arcade
games. The price of arcade games is $1 each.
a. Suppose the cable company has a price of $4 per channel. Draw the budget line, placing TV
channels on the vertical axis. Be sure to label the axes.
channels
new position
12
original position
48 games
b. The following table shows the marginal utilities for different combinations of channels and
games. Fill in the blanks and find the utility maximizing combinations.
Quantities
Channels
Games
Marginal Utility
Channels
Games
Marginal Utility per Dollar Spent
Channels ($4 ea.)
Games($1 ea.)
1
44
50
6
12.5
6
2
40
44
8
11
8
3
36
40
10
10
10
4
32
36
12
9
12
5
28
32
18
8
18
6
24
28
24
7
24
c. Suppose the cable company switches from per channel pricing to a bundle plan: You get six
stations for a cost of $24 per month, but zero stations if you don’t pay the full $24. In other
words, the company tells you to take it (six stations) or leave it (zero stations). Identify the new
budget points on your graph in part a. Does the switch make you worse off or better off?
Explain.
The new bundle is highlighted in red above. It results in lower utility than the original utility
maximizing basket because the utility maximizing condition is no longer satisfied.
Principles of Microeconomics: Problem Set 5
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7. Bill’s favorite dessert is apple pie. After eating apple pie for three days in a row, he decides he wants
banana crème pie instead of apple pie for dessert. Using utility theory, explain why Bill would make
this consumption decision.
Even though Bill’s favorite dessert is apple pie, utility theory predicts Bill will experience diminishing
marginal utility after eating apple pie on consecutive days. There may come a point where the perdollar marginal utility of eating apple pie dips below the per-dollar marginal utility of eating banana
crème pie, in which case Bill will choose to have banana crème pie instead of apple pie.
8. Most newspaper companies allow consumers to purchase copies of the day’s paper by putting money
into a machine and taking out a paper. Why are newspaper companies typically not worried about
consumers putting in 75 cents and taking more than one paper?
A second copy of the same paper has a value of close to zero for customers buying the newspaper.
This is a real-life example of diminishing marginal utility. Because the marginal utility has
diminished to zero, there is no reason for a rational person to take more than one paper.
9. Suppose Chuck’s favorite beverage is cold lemonade and it costs $2 per glass, whereas a bottle of
water costs $1. If Chuck receives 30 utils when he drinks water, how many additional utils would he
need to get from drinking lemonade to cause him to spend the extra dollar it costs to buy it?
We need to equate the marginal utility (MU) per dollar spent for both lemonade and water. MUlemonade
÷ $2 = 30 ÷ $1. Solving for MUlemonade , you get MUlemonade equal to 60 utils. Because the question
asks, “How many additional utils would he [Chuck] need to get from drinking lemonade to cause him
to spend the extra dollar it costs to buy it?” you need to subtract the utils he gets from water from the
utils he gets from lemonade. Thus, the answer is 60 − 30 = 30; 30 additional utils are needed for him
to purchase the lemonade.
10. By using consumer choice theory, explain why diamonds, which are not necessary to sustain life, are
expensive, whereas water, which is necessary for life, is not.
One would think that water, because it is necessary to sustain life, would be very expensive, but for
the most part it is not. The main reason is because in most places water is plentiful, so we take
additional units of it for granted, as well as using it for activities like watering plants or washing
dishes, making the marginal utility not very high. Diamonds, on the other hand, are very limited in
supply. The additional utility an individual gets from each diamond must be really high because of
the high price. This is why diamonds are given for special occasions.
Principles of Microeconomics: Problem Set 5
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