McConnell 22nd edition

1. CHAPTER 7
Utility Maximization

2. 7-2
Law of Diminishing Marginal Utility
Theory of Consumer Behavior
Utility Maximization and the Demand Curve
Income and Substitution Effects
Applications and Extensions
7-2
Chapter Contents

3. 7-3
Terminology
• Utility is the satisfaction one gets from consuming
a good or service.
• Not the same as usefulness
• Subjective: vary from one person to another
• Difficult to quantify
• Sometime measured by “util”, which is one unit of
satisfaction or pleasure.
LO7.1

4. 7-4
Total Utility and Marginal Utility
• Total utility is the total amount of satisfaction.
• Marginal utility is the extra satisfaction from an
additional unit of the good.
MU = ΔTU/ΔQ.
LO7.1

5. 7-5
Graphing Total and Marginal Utility
LO7.1
10
8
6
4
2
0
-2
1 2 3 4 5 6 7
Marginalutility(utils)
MU
Units consumed per meal
(b)
Marginal Utility
0
10
20
30
1 2 3 4 5 6 7
Totalutility(utils)
TU
Units consumed per meal
(a)
Total Utility

6. 7-6
Law of Diminishing Marginal Utility
• Law of diminishing marginal utility: As consumption of a
good or service increases, the marginal utility obtained
from each additional unit of a good or service decreases.
• Example: First slice of pizza gives most satisfaction. The
second slice of pizza gives less satisfaction than the first
one.
• Explains downward sloping demand curve: Consumers are
willing to pay less on additional unit as they consume more
since it gives less satisfaction.
LO7.1

7. 7-7
Theory of Consumer Behavior
• Assumption on Consumer Behavior
• Rational behavior: Consumer wants to get “the most for their
money”
 Utility Maximization
• Three factors affecting consumer’s decision
• Preferences
• Budget constraint
• Prices
• For simplicity, only two goods
LO7.2

8. 7-8
Utility Maximizing Rule
• To maximize satisfaction (utility), consumer allocates his or
her income so that the last dollar spent on each product
yields the same amount of extra (marginal) utility.
• Algebraically,
MU of product A MU of product B
Price of A Price of B
or
MUA / PA = MUB / PB
LO7.2
=

9. 7-9
Consumer Equilibrium
• Consumer can spend his dollar on Product A or Product B.
• “MU of Product/Price” measures utility gain from purchasing
$1 worth of product.
• Satisfaction gain on Product A by spending $1 (MB) is “MU of
Product A/Price of A”.
• Opportunity cost of spending $1 on Product A is loss of
satisfaction from not spending $1 on Product B (MC), which is
“MU of Product B/Price of B”.
• At optimal, MB = MC.

10. 7-10
Reaching Consumer Equilibrium
• If MUA/PA > MUB/PB at current choice, then consumer can increase his
total utility by spending $1 more on Product A and $1 less on Product
B, which results in net gain of total utility by “MUA/PA - MUB/PB”.
• If MUA/PA < MUB/PB at current choice, then consumer can increase his
total utility by spending $1 less on Product A and $1 more on Product
B, which results in net gain of total utility by “MUB/PB - MUA/PA”.
• A rational “utility-maximizing” consumer will stop changing his choice
when he reaches the choice where MUA/PA = MUB/PB, where he
cannot increase his total utility any higher.

11. 7-11
Utility Maximization Example
• A consumer has $10 budget (income) to spend on two
products: Apple and Orange. A price of apple is $1/unit and a
price of orange is $2/unit.
• With $10 budget, the consumer can purchase many different
combinations of Apples and Oranges, where the consumer is
assumed to spend all his budget ($10).
• What combination of Apples and Oranges will provide the
highest satisfaction to the consumer?

12. 7-12
Numerical Example
Table 7.1: The Utility-Maximizing Combination of Apples and Oranges Obtainable with an Income of $10
(2)
Apple (Product A): Price = $1
(3)
Oranges (Product B): Price = $2
(1)
Unit of Product
(a)
Marginal Utility,
Utils
(b)
Marginal Utility per
dollar
(MU/Price)
(a)
Marginal Utility,
Utils
(b)
Marginal Utility per
dollar
(MU/Price)
First 10 10 24 12
Second 8 8 20 10
Third 7 7 18 9
Fourth 6 6 16 8
Fifth 5 5 12 6
Sixth 4 4 6 3
Seventh 3 3 4 2
LO7.2

13. 7-13
Decision-Making Process
Sequence of Purchases to Achieve Consumer Equilibrium, Given the Data in Table 7.1
Choice
Number Potential Choices
Marginal Utility
per Dollar Purchase Decision
Income
Remaining
1 First apple
First orange
10
12
First orange for $2 $8 = $10 – $2
2 First apple
Second orange
10
10
First apple for $1 and
second orange for $2
$5 = $8 – $3
3 Second apple
Third orange
8
9
Third orange for $2 $3 = $5 – $2
4 Second apple
Fourth orange
8
8
Second apple for $1 and
fourth orange for $2
$0 = $3 – $3
LO7.2

14. 7-14
Budget Constraint
• All possible combinations of two goods with $10 budget
where Apple costs $1/unit and Orange costs $2/unit.
Allocation Cost
Apple Orange Apple Orange Total
0 5 $0 $10 $10
2 4 $2 $8 $10
4 3 $4 $6 $10
6 2 $6 $4 $10
8 1 $8 $2 $10
10 0 $10 $0 $10

15. 7-15
Budget Constraint and Optimal Choices
• Among six combinations, purchasing two units of Apple and
four units of Orange gives the highest total utility of 96, where
MUA/PA = MUB/PB = 8.
Budget
Allocation
MU/Price TU
Apple Orange Apple Orange Apple Orange Total
0 5 --- 6 0 90 90
2 4 8 8 18 78 96
4 3 6 9 31 62 93
6 2 4 10 40 44 84
8 1 2 12 45 24 69
10 0 0 --- 46 0 46

16. 7-16
Consumer Equilibrium on Diagram
• MB of spending $1 on Apple (MUA/PA) and MC of not spending $1 on Orange (MUB/PB).
• Consumer equilibrium is reached at MB = MC (MUA/PA = MUB/PB).
MUB/PB (MC)
MUA/PA (MB)

17. 7-17
Change in Price and Optimal Choice
• Price of orange falls
to $1
• Optimal combination
is 4 apples and 6
oranges.
Budget Allocation MU/Price
Apple Orange Apple Orange
0 10 --- 0
1 9 10 1
2 8 8 2
3 7 7 4
4 6 6 6
5 5 5 12
6 4 4 16
7 3 3 18
8 2 2 20
9 1 1 24
10 0 0 ---

18. 7-18
Price per Orange Quantity Demanded
$2 4
1 6
Deriving the Demand Curve
LO7.3
Priceperorange
0
1
$2
4 6
Quantity demanded of oranges
DO
• When price of orange
decreases from $2 to $1,
a consumer increases his
purchase of Orange from
4 units to 6 units.

19. 7-19
Income and Substitution Effects
• Price change has two effects on quantity demanded:
• Income effect: A price increase reduces a consumer’s
real income (after price increase, a consumer can no
longer afford his original combination), and decreases
a quantity demanded.
• Substitution effect: A price increase makes a product
relatively more expensive, and decreases a quantity
demanded (and purchases more of other goods).
LO7.4

20. 7-20
Utility Maximization and the Demand Curve
• Consumer choice based on utility maximization
depends on
• Preferences or tastes (Utility schedule of each product)
• Income (Budget)
• Prices of goods (to find MU per dollar)
• These three are basic determinants of an individual’s
demand.
LO7.3

21. 7-21
Applications and Extensions
• New products (e.g. iPad)
• Diamond-water paradox
• Opportunity cost and time
• Medical care purchases
• Cash and noncash gifts
LO7.5

22. 7-22
Last Word: Rational Criminal Behavior
• The criminal attempts to maximize his or her total utility.
• Compares the marginal benefit with the marginal cost of
the unlawful activity. If MB is greater than MC, a person
may commit a crime as rational choice.
• Most people find the costs too high (e.g. reputation, ethics).
• For others, society imposes additional costs such as fines
and imprisonment, and increases a chance of conviction
through criminal justice system.
• Potential to reduce crime by increasing the cost of crime.