Utility &
Consumer Choice
Review Session
Fall 2026
Utility is the satisfaction you get from consuming
It is personal
The same NC State–UNC ticket gives a die-hard Wolfpack fan many utils and a friend tagging along very few. Unit 5 said it in dollars: willingness to pay differs by person.
It is not money
Utils are not dollars. They are also not a verdict on whether a good is healthy, worthy or important.
Compare within a person
You can rank your own options. You cannot say that your 5 utils are more than your roommate's 3.
Which statement is true?
Given the concepts in this unit, which of the following statements is true?
Choose A, B, C, or D before revealing.
Answer: A · Compare within one person.
A compares your own enjoyment of two activities. B, C, and D compare different people: their utils do not share a common scale, even when the numbers are equal.
Can we add up people's utilities?
Write a short explanation, then compare with a partner.
Think first · explain your reasoning.
No. Utils are not comparable across people.
Utility is personal. We cannot add different people's utils to measure consumer surplus.
From Unit 5, consumer surplus is measured in dollars: willingness to pay minus the price paid, summed over purchased units. Those dollar amounts can be added across buyers.
What is marginal utility?
One more slice of pizza
You have eaten two slices of pizza. You decide to eat a third slice. The extra satisfaction that the third slice adds is its marginal utility.
Total utility
The satisfaction you get from all three slices together.
Marginal utility
The additional satisfaction from eating the third slice after the first two.
Definition: textbook, Consumer Choices, Section 6.1.
Diminishing marginal utility
MU falls, but stays positive
Slices 1–4 add 24, 18, 12, then 6 utils. Each adds less, so TU rises more slowly.
MU reaches zero
The 5th slice adds nothing. TU stays at 60 utils.
MU becomes negative
The 6th slice makes you worse off: MU = −6. TU falls from 60 to 54 utils.
Diminishing MU means smaller additions to TU.
TU falls only when MU becomes negative.
When MU falls, what happens to TU?
What is true for consumers when they choose how much to consume of a good?
Assume MU is positive and diminishing over the range considered.
Answer: A · TU rises while MU falls.
Each extra unit still adds satisfaction, but adds less than the previous unit. If MU reaches zero, TU stops rising; if MU becomes negative, TU falls.
Build total utility from marginal utility
The table shows the marginal utility from drinking cokes.
| Quantity | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Marginal utility | 20 | 15 | 10 | 5 | 0 | −5 |
Start with TU = 0 at zero consumption. Work both parts before revealing.
(a) What is the total utility at 3 units, and what is the marginal utility when you go from 2 cokes to 3 cokes?
TU at 3 = 45 utils; MU of the 3rd coke = 10 utils.
TU = 20 + 15 + 10 = 45. The move from 2 to 3 cokes adds 10 utils.
(b) What is the total utility at 6 units?
TU at 6 = 45 utils.
20 + 15 + 10 + 5 + 0 − 5 = 45. TU reaches 50 at 4 cokes, stays at 50 at 5, then falls to 45 at 6.
One more hour of play
You are playing a game with your friends. The first hour is very fun, adding 20 utils to your total utility. The second hour adds 18 utils. The fifth hour adds 0 utils. Which of the following marginal utilities could be associated with the sixth hour of play?
Assume marginal utility continues to decrease after the fifth hour.
Answer: B · −5 utils.
The fifth hour has MU = 0. With continued diminishing MU, the sixth hour has negative MU and reduces TU. Without this assumption, the earlier values alone do not determine the sixth hour's MU.
When does diminishing MU begin?
You track the marginal utility (MU) you receive from homemade cookies: the first cookie gives MU = 8, the second 10, the third 12, the fourth 9, and the fifth 0. At what point does diminishing marginal utility set in?
Answer: C · From 3 cookies to 4.
MU first rises: 8 → 10 → 12. It first falls from 12 to 9 at the fourth cookie. Diminishing MU begins when MU starts falling, even while MU remains positive.
What can you afford?
The budget line shows bundles that spend the entire budget.
On the line: all income spent.
Inside: money left. Outside: cannot afford.
PxX + PyY = I
José: $56 income, $14 per T-shirt, $7 per movie.
14T + 7M = 56
Intercept = income ÷ price
All T-shirts: 56 ÷ 14 = 4.
All movies: 56 ÷ 7 = 8.
Slope = −Px / Py
Here: −14/7 = −2 movies per T-shirt.
One more T-shirt costs two movies.
Income changes; prices fixed
The line shifts parallel: outward if income rises, inward if it falls.
One price changes; income fixed
The line rotates around the other good's intercept. A price increase rotates it inward.
Read the slope as an opportunity cost
You have $34 per month to spend on entertainment: movies cost $6 each and ice cream costs $4 each. Placing movies on the vertical axis and ice cream on the horizontal axis, which interpretations of the slope of the budget line are correct? (Select all that apply.)
Answer: A and D.
Slope = −4/6 = −2/3 movie per ice cream: A.
The reverse tradeoff is 6/4 = 3/2 ice creams per movie: D.
A price increase: shift or rotation?
A budget line shows your mom's consumption choices between combat boots (vertical axis) and knife throwing (horizontal axis). If the price of knife throwing goes up:
Answer: B · Rotate inward around the vertical intercept.
With income and the price of boots unchanged, the maximum number of boots stays the same. More expensive knife throwing reduces the horizontal intercept. The budget line becomes steeper.
Find the best point on the budget line
Both goods are sold by weight. Drag to change the bundle; keep spending all $24.
Your affordable bundle
MU per dollar
Total utility of the bundle
Rice: MU / price
9.00utils / $MU = 18.00; price = $2/lb
Fruit: MU / price
3.00utils / $MU = 12.00; price = $4/lb
Total utility
148.00utils2 lb rice + 5 lb fruit
Why stop when MU per dollar is equal?
Unequal MU/P means room to improve.
At our starting bundle, rice gives 9 utils/$ and fruit gives 3 utils/$. Move $0.10 from fruit to rice:
Gain ≈ 0.90 utils − give up ≈ 0.30 utils = net gain ≈ 0.60.
Same budget, higher TU. The starting bundle cannot be the best.
The gains shrink; the sacrifices grow.
More rice → rice's MU/P falls.
Less fruit → fruit's MU/P rises.
With diminishing MU, each further shift has a smaller net benefit.
At equal MU/P, that advantage disappears.
At 8 lb rice + 2 lb fruit, both give 6 utils/$ and TU = 184.
Going further makes the utility gained smaller than the utility given up. Moving $1 either way lowers TU to 183.75.
Here: divisible goods, diminishing MU, both goods consumed, and the full budget spent.
Recognize the utility-maximizing rule
Which of the following signals that the consumption choice with the maximum total utility has been selected?
Assume divisible goods, diminishing MU, both goods consumed, and the budget fully spent.
Answer: A · Equal marginal utility per dollar.
If one good gives more utility per dollar, shifting a little spending toward it can raise TU. The rule equalizes MU/P; the two marginal utilities themselves can differ.
Which way should spending move?
You buy only two brands of shoes: Nike and Adidas. The more pairs you buy, the lower the marginal utility of each pair. You spend all of your income. Your MU of a pair of Nikes is 200 and your MU of a pair of Adidas is 120. Nikes cost $100 a pair and Adidas cost $80 a pair. Which statement is true?
For this question, use the continuous-choice approximation: purchases can be adjusted in small amounts.
Answer: B · Shift spending from Adidas toward Nike.
Nike: 200/$100 = 2 utils/$. Adidas: 120/$80 = 1.5 utils/$. A small shift toward Nike gains more utility than it gives up. This describes a spending adjustment, not a one-for-one exchange of shoes.
Use MU/P to recover a price
You like candy and cake. After using your entire $30 budget at the sugar store, you find that the MU of the last candy you consumed was 60 and the MU of the last piece of cake was 30. Assume you have maximized your utility.
Use the equal-MU/P condition at an interior optimum.
(a) What must be true about the prices?
Answer: A · Twice the price.
60/Pcandy = 30/Pcake
Pcandy/Pcake = 60/30 = 2.
(b) If a piece of candy costs $4, what is the price of a piece of cake?
Work out the price before revealing.
Answer: $2 per piece of cake.
Candy: 60/$4 = 15 utils/$.
Cake must also give 15 utils/$:
30/Pcake = 15
Pcake = 30/15 = $2.
Which good became relatively cheaper?
Bundles: (rice lb, fruit lb).
The temporary line still passes through A.
Rice: $2 → $1/lb
Fruit stays $4/lb; income stays $24.
1 lb of fruit now costs 4 lb of rice, up from 2. Rice is relatively cheaper.
Temporarily remove the savings
Old bundle A: 8 lb rice + 2 lb fruit.
It now costs $8 + $8 = $16.
Set aside $8 so A is still just affordable.
A → B: more rice, less fruit
At A, rice's MU/P rises from 6 to 12; fruit's stays at 6. Reallocate toward rice.
The $8 removal is a thought experiment.
Definition: textbook, Consumer Choices, Section 6.2. Compensation keeps the old bundle affordable.
Same income. Greater purchasing power.
Same new prices: rice $1/lb, fruit $4/lb.
The budget lines are parallel.
Put the $8 back
Your actual income never changed: $24.
The old bundle costs only $16, leaving $8. At the new prices, restore that buying power.
What would you buy with more?
Normal good → more.
Inferior good → less.
The direction depends on preferences.
B → C: more of both here
Rice: 12.8 → 14.4 lb.
Fruit: 0.8 → 2.4 lb.
Both are normal for this consumer.
Inferior describes an income response, not quality.
Definition: textbook, Consumer Choices, Section 6.2. A → B: substitution; B → C: income.
Which way does each effect push?
Two goods only. Consider each row as a separate case.
| Good and type | Substitution effect | Income effect | Overall change |
|---|---|---|---|
| Rice: normal | ↑ | ↑ | Increase |
| Rice: inferior | ↑ | ↓ | Depends on strength |
| Fruit: normal | ↓ | ↑ | Depends on strength |
| Fruit: inferior | ↓ | ↓ | Decrease |
If rice's price rises, reverse the effect directions.
When can the income effect overturn the usual result?
If rice is inferior and its income effect is stronger, a lower price can mean less rice consumed: Giffen behavior. Inferior does not automatically mean Giffen.
Textbook, Consumer Choices, Section 6.2. Giffen insight: Jiaming Mao, Giffen Behavior, pp. 4–7 (CC BY-NC 4.0).
Can cheaper rice mean less rice eaten?
Illustrative photo; not a study household.
Photo: Douglas Perkins, CC0.
Evidence: low-income households in Hunan
In this Chinese study, rice-price subsidies led households to eat less rice and more seafood.
Why can this happen?
Rice fills much of the diet when money is tight. Cheaper rice frees up purchasing power, allowing families to eat more preferred foods and rely less on rice.
Connect the two effects
Substitution effect: cheaper rice → more rice.
Income effect: greater buying power → less rice.
The income effect is stronger.
Rice is not a Giffen good for everyone. All Giffen goods are inferior; not all inferior goods are Giffen.
Sources: Jensen & Miller (2008), American Economic Review; J-PAL study summary.
Explain the change in viewing choices
Your two favorite shows are Ted Lasso and Stranger Things. In a normal week, you buy 3 episodes of each. After the price of Ted Lasso increases, you buy only 2 episodes of Ted Lasso and 2 episodes of Stranger Things. This can be explained by:
Assume both shows are normal goods. Choose the explanation that accounts for both effects.
Answer: A.
Ted Lasso: both effects reduce consumption. Stranger Things: substitution pushes consumption up, but the income effect pushes it down more. Its normal-good status alone does not explain the net change.
What does each demand-curve point mean?
Which of the following are true at all points on a demand curve? (Select all that apply.)
Answer: A and B.
Each point shows the utility-maximizing quantity at that price. Income stays fixed along the curve; an income change shifts the curve, so C is false.
Connect marginal utility to demand
The law of diminishing marginal utility helps explain why the demand curve slopes downward because:
Answer: B.
With diminishing MU, additional units are worth less to the consumer, so a lower price encourages more consumption. This is the usual intuition; diminishing MU alone does not rule out Giffen behavior.