AP® Microeconomics review sheet from Aim for Five (aimforfive.com/micro/units/1/1-6)
Unit 1 · Topic 1.6
1.6 Marginal Analysis and Consumer Choice
Marginal analysis means deciding one step at a time: do one more unit only if its extra benefit is at least its extra cost. Consumers use the same idea to split a budget between goods: they get the most total utility when the marginal utility per dollar is equal across goods.
Key terms
- marginal benefit
- marginal cost
- sunk cost
- diminishing marginal utility
- marginal utility per dollar
- utility-maximizing rule
Thinking at the margin
'Marginal' means 'one more'. Marginal benefit (MB) is the extra benefit from one more unit, and marginal cost (MC) is the extra cost of that unit.
The rule: keep doing more of an activity as long as MB is greater than MC, and stop where MB = MC. Before that point, each extra unit adds more benefit than cost, so net benefit grows. Past it, each extra unit costs more than it adds, so net benefit shrinks. With a table of whole units, do every unit where MB ≥ MC and stop before the first unit where MB < MC.
This idea runs through the whole course. Firms use it to choose output (MR = MC, topic 3.5) and hire workers (topic 5.3), and society uses it to judge efficiency (topic 6.1).
Ignore sunk costs
A sunk cost has already been paid and can't be recovered, such as a non-refundable ticket. Since it's gone whatever you do next, it shouldn't change your choice. Only future, avoidable costs and benefits matter at the margin. Sticking with a bad choice because you've 'already paid for it' is called the sunk cost fallacy.
Utility and diminishing marginal utility
Utility is the satisfaction you get from consuming something. Total utility is all the satisfaction from all the units; marginal utility (MU) is the extra satisfaction from one more unit.
The law of diminishing marginal utility says that as you consume more of a good in a period, each extra unit usually adds less satisfaction than the one before. The first slice of pizza when you're hungry is great; the fifth is much less exciting. Total utility keeps rising as long as MU is positive, is at its peak when MU is zero, and falls if MU turns negative (eating so much you feel sick).
The utility-maximizing rule
With a limited budget, you want each dollar to buy as much satisfaction as possible. Compare goods using marginal utility per dollar: MU ÷ price. You maximize total utility when you spend your whole budget and MU of good X ÷ price of X = MU of good Y ÷ price of Y.
If MU/P for X is higher than for Y, the last dollar on X is doing more for you. Buy more X and less Y. Because of diminishing marginal utility, MU of X falls and MU of Y rises as you shift, until the two ratios are equal.
To solve a table problem, list MU/P for every unit of each good, then 'buy' units in order from the highest MU/P to the lowest until the budget runs out. You can't compare raw MU across goods with different prices; always divide by price first.
You won't be tested on indifference curves or budget-line graphs; comparing MU per dollar is what the exam expects.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Using the utility-maximizing rule
Sam has $9 to spend on pizza slices ($2 each) and sodas ($1 each). Pizza MU for slices 1–4: 20, 16, 12, 8. Soda MU for cans 1–5: 10, 8, 6, 4, 2. What combination maximizes Sam's total utility, and what is that total?
Show the solutionHide the solution
- Step 1: Find MU per dollar. Pizza (÷ $2): 10, 8, 6, 4. Soda (÷ $1): 10, 8, 6, 4, 2.
- Step 2: Buy in order of highest MU/P: pizza 1 and soda 1 (10 each) cost $3; pizza 2 and soda 2 (8 each) bring the total to $6; pizza 3 and soda 3 (6 each) bring it to $9.
- Step 3: The budget is used up: 3 × $2 + 3 × $1 = $9. The last units have equal MU/P (6 = 6).
- Step 4: Total utility = (20 + 16 + 12) + (10 + 8 + 6) = 48 + 24 = 72.
Answer: 3 slices and 3 sodas, for a total utility of 72.
- Example 2Calculator allowed
Marginal benefit vs. marginal cost
Lena values hours of studying for a test as follows. Marginal benefit of hours 1–5: 30, 24, 18, 12, 6 points of satisfaction. Each hour has a marginal cost of 15 (the fun she gives up). How many hours should she study?
Show the solutionHide the solution
- Step 1: Hour 1: MB 30 > MC 15, so study it. Hour 2: 24 > 15, study. Hour 3: 18 > 15, study.
- Step 2: Hour 4: MB 12 < MC 15. This hour adds less than it costs, so stop before it.
- Step 3: Net benefit after 3 hours = (30 + 24 + 18) − 3 × 15 = 72 − 45 = 27. After 4 it would be 84 − 60 = 24, which is lower.
Answer: 3 hours.
- Example 3
The sunk cost trap
You paid $60 for a non-refundable concert ticket. On the night, a friend offers you a free ticket to a game you'd enjoy more than the concert. The two events are at the same time. Which should you choose?
Show the solutionHide the solution
- Step 1: The $60 is sunk: you lose it whether you go to the concert or not.
- Step 2: Compare only what's still ahead: the game gives you more enjoyment, and both cost you the same evening.
- Step 3: Choose the game. Going to the concert just because you paid for it is the sunk cost fallacy.
Answer: Go to the game; the $60 is a sunk cost and shouldn't affect the choice.
Common mistakes
- Comparing marginal utility without dividing by price. A good with higher MU can still be the worse buy if it costs much more.
- Stopping where total utility or total benefit is highest instead of where MB = MC. More total benefit isn't worth it if the extra cost is higher still.
- Thinking diminishing marginal utility means total utility falls. Total utility keeps rising as long as MU is positive; it just rises more slowly.
- Forgetting to spend the whole budget. Equal MU/P ratios only maximize utility when all the income is used.
On the exam
- Expect a table of marginal utilities and prices with a budget; you'll be asked for the utility-maximizing combination or which good to buy more of. Show MU/P for each unit.
- Questions about marginal decisions often hide a sunk cost in the story. Cross it out before you compare marginal benefit and marginal cost.
Connected topics
Videos
Check yourself
5 questions on 1.6 Marginal Analysis and Consumer Choice. Pick an answer to see if you got it, and why.
| Hour of studying | Marginal benefit | Marginal cost |
|---|---|---|
| 1st | 20 | 4 |
| 2nd | 16 | 6 |
| 3rd | 12 | 8 |
| 4th | 8 | 10 |
| 5th | 4 | 12 |
Hypothetical benefits and costs of studying, in points of satisfaction
A student uses marginal analysis to decide how many hours to study. How many hours should the student study?
What is the student's total net benefit from studying the best number of hours?
Jordan paid $60 for a nonrefundable concert ticket. On the night of the concert, a friend offers Jordan free tickets to a basketball game that Jordan would enjoy more than the concert. What should Jordan do?
| Slices of pizza | Total utility (utils) |
|---|---|
| 0 | 0 |
| 1 | 30 |
| 2 | 50 |
| 3 | 62 |
| 4 | 68 |
| 5 | 68 |
Hypothetical utility from pizza for one person
What is the marginal utility of the third slice of pizza?
Which of the following best describes what the table shows?
0 of 5 answered