Chapter 07 – Utility Maximization
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Chapter 07 – Utility Maximization
McConnell Brue Flynn 21e
DISCUSSION QUESTIONS
1. Complete the following table and answer the questions below: LO1
a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate?
How do you know?
b. “A rational consumer will purchase only 1 unit of the product represented by these data since
that amount maximizes marginal utility.” Do you agree? Explain why or why not.
c. “It is possible that a rational consumer will not purchase any units of the product represented
by these data.” Do you agree? Explain why or why not.
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2. Mrs. Simpson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents,
respectively. At present she is buying these products in amounts such that the marginal utilities
from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying
the utility-maximizing combination of bread and milk? If not, how should she reallocate her
expenditures between the two goods? LO2
3. How can time be incorporated into the theory of consumer behavior? Explain the following
comment: “Want to make millions of dollars? Devise a product that saves Americans lots of
time.” LO2
Answer: Time is money. This expression is a time-saving way of making the point that
4. Explain: LO2
a. Before economic growth, there were too few goods; after growth, there is too little time.
b. It is irrational for an individual to take the time to be completely rational in economic decision
making.
c. Telling your spouse where you would like to go out to eat for your birthday makes sense in
terms of utility maximization.
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Answer:
5. In the last decade or so there has been a dramatic expansion of small retail convenience stores
(such as 7 Eleven, Kwik Shop, and Circle K), although their prices are generally much higher
than prices in large supermarkets. What explains the success of the convenience stores? LO2
Answer: These stores are selling convenience as well as the goods that are purchased
6. Many apartment-complex owners are installing water meters for each apartment and billing the
occupants according to the amount of water they use. This is in contrast to the former procedure
of having a central meter for the entire complex and dividing up the collective water expense as
part of the rent. Where individual meters have been installed, water usage has declined 10 to 40
percent. Explain that drop, referring to price and marginal utility. LO3
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7. Using the utility-maximization rule as your point of reference, explain the income and
substitution effects of an increase in the price of product B, with no change in the price of product
A. LO4
Answer: The utility-maximization rule compares the marginal utilities per dollar of goods
8. ADVANCED ANAYLSIS A “mathematically fair bet” is one in which the amount won will
on average equal the amount bet, for example when a gambler bets, say, $100 for a 10 percent
chance to win $1,000 ($100 = .10 x $1,000). Assuming diminishing marginal utility of dollars,
explain why this is not a fair bet in terms of utility. Why is it even a less fair bet when the
“house” takes a cut of each dollar bet? So is gambling irrational? LO4
Answer: Because the marginal utility of money diminishes the more you have, the utility
9. Rank each of the following three gift possibilities in terms of how much utility they are likely
to bring and explain your reasoning.  A store-specific gift card worth $15, a $15 item from
that specific store, and $15 of cash that can be spent anywhere. LO5
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Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
item. The cash gives him the ability to select how the money is spent, and he can
therefore purchase the item he values the most. The more say that the recipient has on
how the money is spent, the more likely the option will have a higher utility.
10. LAST WORD In what way is criminal behavior similar to consumer behavior? Why do
most people obtain goods via legal behavior as opposed to illegal behavior? What are society’s
main options for reducing illegal behavior?
Answer:
REVIEW QUESTIONS
1. True or false. The law of diminishing marginal utility predicts the consumption behavior of
addicts quite well. LO1
2. Frank spends $75 on 10 magazines and 25 newspapers. The magazines cost $5 each and the
newspapers cost $2.50 each. Suppose that his MU from the final magazine is 10 utils while his
MU from the final newspaper is also 10 utils. According to the utility-maximizing rule, Frank
should: LO2
a. Reallocate spending from magazines to newspapers.
b. Reallocate spending from newspapers to magazines.
c. Be satisfied because he is already maximizing his total utility.
d. None of the above.
Chapter 07 – Utility Maximization
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Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
Answer: a, reallocate spending from magazines to newspapers
Frank is not currently maximizing the utility that he could get from his $75 budget and
should reallocate spending from magazines to newspaper in order to increase the total
utility that he receives from his budget.
This can be seen by examining the MU per dollar that he is currently getting from the last
magazine and the last newspaper. The MU per dollar from the last magazine is 10/$5 = 2
utils per dollar. The MU per dollar from the last newspaper is 10/$2.50 = 4 utils per
dollar. Thus, Frank could gain more total utils if he spent less on newspapers and more
on dollars.
As an example, imagine that Frank cut his purchases of magazines by one, reducing them
from 10 purchased to only 9 purchased. That would free up $5 that he could spend on
newspapers. Since newspapers cost $2.50 each, he could purchase two newspapers.
Now, look at what happens to his total utility as he makes that change in consumption.
He will lose 10 utils by consuming one fewer magazine (because the MU of magazines is
10). But he will gain more than 10 utils by consuming two additional newspapers
(because the MU of an additional newspaper is 10 utils and he will be consuming two
additional newspapers). Thus, by reallocating his spending from the product with the
lower MU per dollar to the product with the higher MU per dollar, Frank will be able to
increase the total utility that he receives from his budget.
3. Demand curves slope downward because, other things held equal, LO3
a. An increase in a product’s price lowers MU.
b. A decrease in a product’s price lowers MU.
c. A decrease in a product’s price raises MU per dollar and makes consumers wish to purchase
more units.
d. An increase in a product’s price raises MU per dollar and makes consumers wish to purchase
more units.
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4. Jermaine spends his money on cucumbers and lettuce. If the price of cucumbers falls, the MU
per dollar of cucumbers will ______________ and Jermaine will _______________ cucumbers
for lettuce. LO4
a. Fall; substitute
b. Rise; substitute
c. Fall; supply
d. Rise; demand
5. Tammy spends her money on lemonade and iced tea. If the price of lemonade falls, it is as
though her income __________________. LO4
a. increases
b. decreases
c. stays the same
Answer: a, increases.
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PROBLEMS
1. Mylie’s total utility from singing the same song over and over is 50 utils after one repetition,
90 utils after two repetitions, 70 utils after three repetitions, 20 utils after four repetitions, –50
utils after five repetitions, and -200 utils after six repetitions. Write down her marginal utility for
each repetition. Once Mylie’s total utility begins to decrease, does each additional singing of the
song hurt more than the previous one or less than the previous one? LO1
2. John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two
Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does
John show diminishing marginal utility for Coke or does he show increasing marginal utility for
Coke? Suppose that John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend
one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke,
too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no
matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke? LO1
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Feedback: Consider the following values: After consuming one Coke, John has a total
utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he
has a total utility of 50 utils. Also, assume John has $3 in his pocket and Cokes cost $1
3. Suppose that Omar’s marginal utility for cups of coffee is constant at 1.5 utils per cup, no
matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for
the first doughnut he eats, 9 for the second he eats, 8 for the third he eats, and so on (that is,
declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup,
doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or
both. How big would that budget have to be before he would spend a dollar buying a first cup of
coffee? LO2
Chapter 07 – Utility Maximization
4. Columns 1 through 4 in the table below show the marginal utility, measured in utils, that
Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows
the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are,
respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. LO2
a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility?
b. How many dollars will Ricardo choose to save?
c. Check your answers by substituting them into the algebraic statement of the utility-maximizing
rule (verify that all of the income has been exhausted between the various goods and savings).
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The table above reads across rows (for example, the first row labeled ‘Column 1–Good A’
is marginal utility per dollar for good A). The columns represent the marginal utility per
dollar for the different goods for each unit consumed and saving (for example, column 1
‘Marginal Utility per dollar unit 1’ tells us the marginal utility per dollar for the first unit
of every good and savings). This will makes the comparison a little easier.
5. You are choosing between two goods, X and Y, and your marginal utility from each is as
shown in the table below. If your income is $9 and the prices of X and Y are $2 and $1,
respectively, what quantities of each will you purchase to maximize utility? What total utility will
you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What
quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a
demand schedule (prices and quantities demanded table) for X. LO3
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Feedback: Consider the following table and information as an example:
Your income is $9 and the prices of X and Y are $2 and $1, respectively.
The first step is to convert the marginal utility values into marginal utility per dollar
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First, we only consider the first two rows for Goods X and Y for the first price of good X
(price of X is $2). We purchase the first unit of good Y with a marginal utility per dollar
of 8. Next we purchase the second unit of good Y with a marginal utility per dollar of 7.
6. ADVANCED ANAYLSIS Let MUA = z = 10 – x and MUB = z = 21 – 2y, where z is marginal
utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent
on product B. Assume that the consumer has $10 to spend on A and B—that is, x + y = 10. How
is the $10 best allocated between A and B? How much utility will the marginal dollar yield? LO3
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7. Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when
sushi costs $2 per piece and bagels cost $2 per bagel. But then, after the price of bagels falls to $1
per bagel, she spends $50 on sushi and $50 on bagels. How many pieces of sushi and how many
bagels did Deborah consume before the price change? At the new prices, how much money
would it have cost Deborah to buy those same quantities (the ones that she consumed before the
price change)? Given that it used to take Deborah’s entire $100 to buy those quantities, how big is
the income effect caused by the reduction in the price of bagels? LO4