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Module
20
Maximizing Utility
Module Objectives
Students will learn in this module:
• Why consumers’ general goal is to maximize utility. • Why the principle of diminishing marginal utility applies to the consumption of most
goods and services.
• How to use marginal analysis to find the optimal consumption bundle.
Module Outline
I.Utility: It’s All About Getting Satisfaction
A.Utility and consumption
1. Definition: Utility is a measure of personal satisfaction.
2. An individual’s consumption bundle is the collection of all the goods and
services consumed by an individual.
3. An individual’s total utility function gives the total utility generated by his
or her consumption bundle.
4. Definition: A util is a unit of utility.
B.The principle of diminishing marginal utility
1. Definition: The marginal utility of a good or service is the change in
total utility generated by consuming an additional unit of that good or
service.
2. Definition: The marginal utility curve shows how marginal utility
depends on the quantity of a good or service consumed.
3. Definition: The principle of diminishing marginal utility says that
each successive unit of a good or service consumed adds less to total utility than the previous unit.
4. There are a few exceptions to the principle of diminishing marginal utility: goods that you must gain experience to enjoy (skiing) and goods that
deliver satisfaction only if you buy enough of them (wallpaper), so marginal utility increases before it begins to diminish. II.Budgets and Optimal Consumption
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A.Budget constraints and budget lines
1. Definition: A budget constraint requires that the cost of a consumer’s
consumption bundle is no more than the consumer’s total income.
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2. Definition: A consumer’s consumption possibilities is the set of all
consumption bundles that he or she can consume given the consumer’s
income and prevailing prices.
3. The consumption bundle that a consumer actually buys depends on the
consumer’s income and the prices of the goods and services as illustrated
in Figure 20-2 below.
4. Definition: A consumer’s budget line shows the consumption bundles
available to a consumer who spends all of his or her income.
5. Every consumption bundle on or inside the budget line is affordable,
while every bundle outside the budget line is unaffordable.
The Budget Line
Consumption
bundle
Quantity
of potatoes
(pounds)
10
Unaffordable
consumption bundles
A
8
B
6
4
2
0
A
B
C
D
E
F
C
Affordable
consumption
bundles
2
Quantity
of potatoes
0
1
2
3
4
5
10
8
6
4
2
0
(pounds)
(pounds)
Affordable consumption
bundles that cost all of
Sammy’s income
D
E
F
1
Quantity
of clams
3
4
Sammy’s budget line, BL
5
Quantity of clams (pounds)
B.The optimal consumption bundle
1. Definition: The optimal consumption bundle is the consumption
bundle that maximizes a consumer’s total utility, given his or her budget
constraint.
2. An individual’s optimal consumption bundle is the one that maximizes
total utility, and so puts the individual at the top of his or her total utility
curve.
III.Spending the Marginal Dollar
A.Marginal utility per dollar
1. Definition: The marginal utility per dollar spent on a good or service is
the additional utility from spending one more dollar on that good or
service.
2. When deciding to purchase a good, a consumer weighs the additional
utility to be derived from the good against the additional cost (price) of
the good.
3. MUC and MUP indicate the marginal utility of clams and potatoes,
respectively.
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4. The marginal utility per dollar of clams = MUC/PC, and the marginal utility per dollar of potatoes = MUP/PP.
B.Optimal consumption
1. Definition: The optimal consumption rule states that when a consumer maximizes utility, the marginal utility per dollar spent must be the
same for all goods and services in the consumption bundle.
2. In equation form, the optimal consumption rule for two goods C and P is
MU C MU P
=
PC
PP
3. If the ratios of the two goods are not equal, consumers will adjust their
choices until the marginal utilities per dollar spent for each and every
good or service in that bundle are equal.
Teaching Tips
Utility: It’s All About Getting Satisfaction
Creating Student Interest
Bring a supply of small treats to class (for example, a box of “doughnut holes” works
well in a morning class). Ask for a volunteer who enjoys the treat you have brought.
Tell them that you will give them the treats in return for data you can use in the class.
Give them a treat (say, a doughnut hole) and let them eat it. They ask the student for
your data—ask, “How much did you like the doughnut hole?” Then student will probably ask you for more information, such as, “compared to what?” or “on what scale?”
Tell them that they agreed to give you the data in return for the doughnut hole and
press them to give you the answer. After making the student squirm for a bit, explain
that the satisfaction received from consuming a good is measured in “utils,” or units
of utility. Then ask the student “how many units of utility did you receive from eating the doughnut hole?” The student may still not want to answer. Encourage them by
pointing out that they are the only one who knows the answer and they have promised
to give you the data. Eventually you should be able to get a number from them. Record
the data on the board and then give them another doughnut hole. Repeat the process.
The number they give will eventually decline. At some point, the student will refuse an
additional doughnut. Coax them to eat as many as they will. When they won’t eat any
more, ask them why. Eventually you will get at the idea that their utility is 0 (or negative). Sometimes students will say they don’t want to eat more because they are thirsty
from the doughnut holes. If you like, bring something for them to drink (say, orange
juice) and discuss complements! Once your final data is recorded, calculate total utility
and graph total and marginal utility.
If you don’t want to bring food to class, or if you have no volunteers for the exercise,
talk about what happens when you are really hungry and you order a pizza. Do you eat
more than one slice? Do you get the same satisfaction from each slice? Is it possible that
the last slice actually gave you negative satisfaction (after the fact)?
Presenting the Material
Show students how marginal utility is calculated (we are assuming that utility can be
quantified). Use the example of determining the marginal utility of bags of peanuts for
Sergio, who has a budget of $12.
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Quantity of bags of peanuts
0
1
Total utility for Sergio
0
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maximizing utility
Marginal utility
—
10(∆TU/∆Q)
2
19
9
3
27
8
4
34
7
5
40
6
The table above demonstrates the law of diminishing marginal utility.
Students are often mystified by the whole concept of attaching a number to how much
they like something. Explain that the numbers are useful for explaining how consumers
make decisions. Point out that the number itself does not matter, just the ranking. As
long as they can tell you that bundle A is preferred to bundle B, then bundle A must have
a higher utility number. The relative value of the numbers matters also. If you like brand
A twice as much as brand B then the marginal utility from brand A should be twice that
of brand B. Ask them what happens if you like the two brands equally? Which one do
you buy?
Budgets and Optimal Consumption
Creating Student Interest
Ask students if they have a budget constraint. What determines their budget constraint?
Does everyone have a budget constraint? Is it possible to consume beyond your budget
constraint? If so, for how long? Students may say that credit cards or other sources of
credit can allow them to consume beyond their budget constraint. If they do, point out
that that can’t go on forever and ask them what it does to their budget constraint in the
future if they run up their credit card today (it will decrease it when the credit card must
be paid off or they suffer the effects of defaulting). Ask them if they think everyone has
a budget constraint.
Presenting the Material
Return to the example of “bags of peanuts for Sergio” presented above.
Construct the budget line. Now have Sergio choose between the quantities of two goods,
peanuts and Cokes. His budget is $12, the price of a bag of peanuts is $2, and the price
of a Coke is $1. Explain that the vertical intercept is found by $12/2, and the horizontal
intercept is found by $12/1.
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Quantity of
bags of
peanuts
6
Budget line
12
Quantity of Cokes
Sergio’s possible consumption bundles, given his budget constraint and the prices of the
products and assuming that he is consuming a bundle on his budget line, are as follows
(any of these combinations can be found on the budget line):
Possible consumption bundle
Quantity of peanuts (in bags)
Quantity of
Cokes
A
012
B
110
C
28
D
36
E
44
F
52
G
60
Spending the Marginal Dollar
Creating Student Interest
Present the class with the following scenario: Each of them has $10 to spend on either
Oreos or Chips Ahoy cookies. Ask them which they would buy, and why. There will
probably be discussion of the different characteristics of the cookies (the tastiness of the
creamy center filling versus the chocolate chips) and who likes which kind of cookie and
why. If during the discussion no one asks how much each type of cookie costs, announce
to the class, “Oh, I forgot, Oreos cost 50 cents each and Chips Ahoy cookies cost $5
each.” Ask if this changes their decision. If anyone hates Oreos, they will not change
their decision. However, anyone who is willing to substitute Oreos for Chips Ahoy cookies will change their decision.
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Presenting the Material
Return to the peanut example used earlier of how marginal utility per dollar is calculated.
Quantity of bags of peanuts
Total utility for Sergio
Marginal utility
Marginal utility
per dollar
0
0
——
1
10
2
19
9
9/2 = 4.5
3
27
8
8/2 = 4
4
34
7
7/2 = 3.5
5
40
6
6/2 = 3
10(∆TU/∆Q)
10/2 = 5
Now have Sergio choose among different combinations of bags of peanuts and Cokes. He
has only $12.00 to spend, the price of peanuts is $2, and the price of Coke is $1. Walk
students through the process of buying the product that has the highest marginal utility
per dollar first; continue until the budget is fully spent.
Quantity of bags of
Total
Marginal
peanuts
utility
utility
0
0
—
Marginal
Marginal
utility
Quantity Total
Marginal utility
per dollar
of Cokes utility
utility per dollar
—
0
0
—
—
1
10
10 10/2 = 5 1
8
(will buy
3rd)
8
8 (will
buy 1st)
2
19
9
9/2 = 4.5 2
14
(will buy 4th)
6
6 (will
buy
2nd)
3
27
8
8/2 = 4
(will buy 3
18
4
4 (will
5th or 6th)
buy
5th or
6th)
4
34
7
7/2 = 3.5
(will buy 7th) 4
21
3
3 (will buy
8th)
2
2
5
40
6
6/2 = 3
5
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The optimal bundle at which Sergio spends the entire $12 budget will be four Cokes and
four bags of peanuts. (Point out that the marginal utility per dollar on the last units
consumed of both goods is roughly equal.)
Common Student Pitfalls
• All income is spent. Students may ask why a consumer cannot choose a consumption bundle within the budget constraint. Explain that in these exercises we
assume that the consumer maximizes utility but receives zero utility from saving
money.
• The “right” marginal comparison—marginal utility versus marginal utility
per dollar. Students often say that a consumer will buy the good with the highest
marginal utility rather than the highest marginal utility per dollar. Remind them
that consumers look at two things: how much extra utility they will receive from
consuming a good and the price of the product. The marginal utility per dollar
incorporates both of these factors.
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Case Studies in the Text
Economics in Action
Buying Your Way Out of Temptation—Consumers will pay more to get less when they gain
utility from smaller portions (they are removed from the temptation to overeat).
Ask students the following questions:
1. Why are consumers willing to pay more for a smaller portion of a product? (They are paying for help in restraining their tendency to overeat.)
2. Why don’t consumers simply save money by buying the larger packages
and separating them into smaller portions placed in Ziploc bags? (They
are willing to pay to save the effort required to separate the portions—the
convenience is worth the higher price.)
Activities
Measuring Marginal Utility of M&M’s (10–15 minutes)
Bring a bag of M&M candies to class and ask if anyone gets satisfaction from them.
Ask a student who derives satisfaction from M&M’s to come to the front and rate each
piece of candy on a marginal utility scale of 1 to 10, with 10 being the highest. Then
hand the student one candy from the bag and have him or her eat the candy and assign
a number for its marginal utility. Do the same with subsequent candies until the law of
diminishing marginal utility is demonstrated.
Understanding Utility (3–5 minutes)
Pair students and ask them to discuss the following issue: Are people today more constrained by time or money? Why do people buy so many cookbooks and spend so little
time cooking? Use the marginal utility theory to explain. (The importance of time
in consumption decisions has been explored by Linder in his book The Harried Leisure
Class. He argues that as economies become wealthier, people are more constrained by
time than by money. One of the implications of his theory is that people substitute buying things for actually doing things.)
Calculating the Optimal Consumption Bundle (5–10 minutes)
Pair students and put the table on page 122 on the board or overhead.
1. Have each pair calculate the optimal consumption bundle when Sergio’s
income is $9. (The optimal consumption bundle is 3 bags of peanuts and 3
Cokes).
2. Ask students to construct the old and new budget lines.
The Overspent American (10–15 minutes)
Separate the class into two groups. Within each group, students should form pairs. Pairs
on one side of the room brainstorm arguments in favor of the following proposition:
According to Juliet Schor in her book The Overspent American, Americans are practitioners of conspicuous consumption and go broke trying to keep up with folks at the top of
the income ladder, make irrational purchases, and deny the amount of credit-card debt
they have, even to themselves. The most visible forms of wealth they desire are expensive
homes and splashy cars, which they cannot afford.
The other side of the room brainstorms arguments in favor of the following argument:
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In the book The Two Income Trap, authors Elizabeth Warren and Amelia Warren Tyagi
argue that Americans are filing for bankruptcy in higher numbers than ever before
because the cost of a home today takes up so much of discretionary spending. They argue
that Americans are not spending irrationally. Rather, parents bid against one another
for housing in better school districts. Higher mortgage payments, combined with higher
medical expenses and rising college tuitions, are leaving two-income earner families
broke. Ask students on each side of the room to discuss with a partner whether the excerpt
accurately describes middle-class consumers. These pairs now break up and find a partner
from the other side of the room. Ask each student to share the excerpt with his or her
new partner. As a pair, students now discuss which description of middle-class consumers seems the most accurate. Ask a few pairs to report.
Buying a New Car (5–10 minutes)
Tell students they need to buy a new car. Ask them to write down two choices. One is
the sensible and reliable choice and the other is the dream car. Now ask them to think
about the marginal utility they would get from each car. How many times more satisfaction would they get from the dream car? Press them to come up with a number. Now ask
them to estimate the price of each car and calculate marginal utility per dollar. Someone
in class with a computer could go to Edmunds.com and look up price data for the class.
Which car do they buy? Ask students to share their results.
Web Resources
The following websites may provide useful information for students:
Personal Finance and Education Information from the Chicago Federal Reserve Bank:
http://www.chicagofed.org/webpages/education/index.cfm
Money Instructor web page on budgeting (including information and curriculum):
http://www.moneyinstructor.com/budgeting.asp.
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