1. Mod 51-Utility Maximization
Duffka School of Economics

2. Student learning objectives:
• How consumers make choices about the purchase of goods and services
• Why a consumer’s goal is to maximizing 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.

3. Key Economic Concepts For This Module:
• Consumers receive happiness, or utility, when they consume goods and services.
• As more and more of a good is consumed, the additional, or marginal utility received from the next unit falls. This is the principle of diminishing marginal utility.
• Consumers are faced with a budget constraint and within that constraint they purchase items such that their total utility is maximized.
• The consumer has maximized his/her utility by consuming all of their income to the point where the marginal utility per dollar is equal across all goods.

4. Class Presentation of Module
I. Utility: It’s All About Getting Satisfaction
A. Utility and Consumption
B. The Principle of Diminishing Marginal Utility
II. Budgets and Optimal Consumption
A. Budget Constraints and Budget Lines
B. The Optimal Consumption Bundle
III. Spending the Marginal Dollar
A. Marginal Utility per Dollar
B. Optimal Consumption

5. I. Utility: It’s All About Getting Satisfaction
Why do we demand particular goods and services?
Because they make us happy and because we can afford them. Economists refer to this happiness as utility.
Utility is a measure of the satisfaction the consumer derives from consumption of goods and services.
Utility is a subjective notion in economics, we don’t expect to really measure it, but consumers know when utility is rising or falling, and they know when one choice provides more utility than another.

6. I. Utility: It’s All About Getting Satisfaction

7. A. Utility and Consumption
We get utility from many things, and everything you buy constitutes your consumption bundle.
But for now, we focus on one good, holding all others equal.
Example Consumption, Total, and Marginal Utility

8. B. The Principle of Diminishing Marginal Utility
Most of the time we make consumption decisions incrementally.
For example: Should I consume a 3rd Slurpee, after already having 2 this week?
The answer is simple: yes, if the third Slurpee increases my total utility.
The incremental change (an addition or a subtraction) to total utility is called marginal utility.
MU = Δ TU /ΔX
TU of 2 slurpees = 70 happy points.
TU of 3 slurpees = 90 happy points.
MU of the 3rd slurpee = (90 – 70)/1 = 20 additional happy points.

9. B. The Principle of Diminishing Marginal Utility
The MU function slopes downward due to the Principle of Diminishing Marginal Utility.
Principle of DMU: the additional satisfaction a consumer gets from one more unit of a good or service declines as the amount of that good or service consumed rises.

10. II. Budgets and Optimal Consumption
Consumers want to maximize utility, but must do so within a budget constraint. This is described as “constrained utility maximization”.
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
2. Choose the bundle that provides the highest utility.

11. A. Budget Constraints and Budget Lines
Points inside the line are affordable, but do not use all of the consumer’s income
Points outside the budget line are unaffordable.
Points along the budget line are affordable and all of the income is spent.

12. B. The Optimal Consumption Bundle
We need to focus only on the combinations that lie upon the budget line

13. III. Spending the Marginal Dollar
A. Marginal Utility Per Dollar
MU = ΔTU/ΔX and to get MU per dollar, we just divide this by the price.

14. B. Optimal Consumption
The optimal consumption rule says that in order to maximize utility, a consumer must equate the marginal utility per dollar spent on each good and service in the consumption bundle.

15. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Part A: Figure Marginal Utility of Polo Shirts & Steaks
# of Polo Shirts
Total Utility
Marginal Utility
# of Steaks 1 60 20 2
100 36 3
130 51 4
150 65 5
165 78 6
175 90 60 20 40 16 30 15 20 14 15 13 10 12

16. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Figure Total & Marginal Utility of Polo Shirts and Steaks
Total Utility
Total Utility
# of Polo Shirts
# of Steaks
Marginal Utility
Marginal Utility
# of Polo Shirts
# of Steaks

17. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
3. Looking at the chart & graphs, you can conclude:
A. Total utility is always (increasing/decreasing).
B. Marginal utility initially (increases/decreases) and eventually (increases/decreases).

18. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
MUx = MUy
Px Py
Us e the info in 11.3 to analyze Frank’s choice between gas and food. He has an income of $130, gas is $10/gallon, and food is $20.
Gas
Mug
MUg/Pg
Food
MUf
MUf/Pf 1 60
6.0
115
5.75 2 55
105 3 51 98 4 48 94 5 47 92 6 46 90
5.5
5.25
5.1
4.90
4.8
4.70
4.7
4.60
4.6
4.5

19. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Figure 11.3
A. Does the combo G =1 & F=6 satisfy the income constraint?
YES
Can Frank purchase this combination of goods with his income?
B. Is this the utility maximizing combination of goods? NO
C. In which direction would Frank like to reallocate his purchases?
Buy less food and more gas
D. What is Frank’s maximizing combination of goods, subject to the income constraint?
4 Food and 5 Gasoline

20. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Part C: Figure 11.4
5. Marginal utility of 3rd CD?
6. Joel’s CS if $11/each?
7. What would happen to Joels’ CS if he buys an additional $11?
8. How many CDs should Joel $11?
9. What is Joels the optimal #?
10. If CDs go on sale & P drops to $8 Q?
# CD’s
Total Utility 1
$25 2
$45 3
$63 4
$78 5
$90 6
$100 7
$106 8
$110
Marginal
Utility
$11
$18 25 14
$30 20 9 18 7
D. Consumer surplus increases by $4 15 4
C. 5 12 1
A. $35 10 -1 6 -5
B.6 4 -7

21. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
11. Why is consumer surplus important?
Because MARKETS create consumer surplus, many consumers buy the good for less than they would be willing to pay. Consumers like this, but businesses would like to price the goods to collect consumer surplus.

22. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Part C explained how consumer surplus and marginal utility create a downward sloping demand curve.
Part D: Income and Substitution Effects
Income Effect: When the P of a good falls, consumers experience an increase in purchasing power. When the P of a good increases, consumers experience a decrease in purchasing power.
Substitution Effect: When the P of a good changes, consumers will substitute toward the now relatively less expensive good.

23. APE U2 L1 A11 Why is a Demand Curve Downward Sloping?
Income Effect: When the P of a good falls, consumers experience an increase in purchasing power. When the P of a good increases, consumers experience a decrease in purchasing power.
Substitution Effect: When the P of a good changes, consumers will substitute toward the now relatively less expensive good.
The P of a burger has increased, but the P of the chicken sandwich stays the same. You typically buy both.
12. How will the increase in the P of a burger affect the purchase of burgers?
Buy fewer burgers b/c they are RELATIVELY more expensive than chicken.
13. Describe how the substitution effect changes your purchases.
B/c the P of burgers increased, chix is relatively less expensive. Therefore, you sub chix for burgers.
14. Describe how the income effect changes your purchases.
The increase in the P of burgers is the same as if you had a decrease in real income or purchasing power. Therefore, you would buy fewer burgers.

24. Activity
At the beginning of the hour, think carefully about your current level of happiness or well-being. Are you having a great day, or a crummy day? Judge your level of well-being on a scale of 0 – 100 where 0 is the worst day of your life and 100 is absolute bliss. Enter this assessment of your well-being on the first row of the table below. Economists refer to happiness as utility.
You will be given one candy at a time. If you wish to consume the candy, do so, and reevaluate your happiness. Enter this number in the table. If you consume a second candy, do so, and reevaluate your utility. Important! Do not eat an additional candy until you have reevaluated your utility from the most recent. You may stop eating at any time.

25. Practice question #1
1. Generally, each successive unit of a good consumed will cause marginal utility to
a. increase at an increasing rate.
b. increase at a decreasing rate.
c. increase at a constant rate.
d. decrease.
e. either increase or decrease.

26. Practice question #2
2. Assume there are two goods, good X and good Y. Good X costs $5 and good Y costs $10. If your income is $200, which of the following combinations of good X and good Y is on your budget line?
a. 0 units of good X and 18 units of good Y
b. 0 units of good X and 20 units of good Y
c. 20 units of good X and 0 units of good Y
d. 10 units of good X and 12 units of good Y
e. all of the above

27. Practice question #3
3. The optimal consumption rule states that total utility is maximized when all income is spent and
a. MU/P is equal for all goods.
b. MU is equal for all goods.
c. P/MU is equal for all goods.
d. MU is as high as possible for all goods.
e. The amount spent on each good is equal.

28. Practice question #4
4. A consumer is spending all of her income and receiving 100 utils from the last unit of good A and 80 utils from the last unit of good B. If the price of good A is $2 and the price of good B is $1, to maximize total utility the consumer should buy
a. more of good A.
b. more of good B.
c. less of good B.
d. more of both goods.
e. less of both goods.

29. Practice question #5
5. The optimal consumption bundle is always represented by a point
a. inside the consumer’s budget line.
b. outside the consumer’s budget line.
c. at the highest point on the consumer’s budget line.
d. on the consumer’s budget line.
e. at the horizontal intercept of the consumer’s budget line.

30. Activity

31. Activity
To focus on the effect that eating candy had on your utility, create a third column that subtracts the initial utility from each row in the table. So if you had an initial utility of 80 and eating one candy caused your utility to be 85, subtract 80 from that value and the first candy gave you 5 happy points. You can see that utility from candy when you have had zero candies must equal zero.
When you have finished eating candy, construct a simple graph. Put total utility from candy on the y-axis and candy on the x-axis. Plot your points from the table above.

32. Activity Discussion Questions
You didn’t have to purchase each candy, so why did you stop eating?
Imagine you had eaten one more candy. Hypothetically reevaluate your total utility.
Define Marginal Utility:
The change in total utility generated by consuming one additional unit of that good.
Complete the final column in the table and plot on a new graph.
Is your MU graph falling? Why or why not?
Explain the Principle of Diminishing MU:
each successive unit of a good consumed adds less to total utility than the previous unit.
What is the marginal utility of that hypothetical candy that you would not have eaten?
Have you ever done something (like eaten too much candy) where you experienced negative MU? What happened?