Microeconomics guide, Unit 1, step 5 of 28Previous step Next step

Step 5: Marginal Analysis and Consumer Choice

By the EconTutorials team. 11-minute read with 6 practice questions.

SyllabusAP Micro 1.5–1.6 · Cambridge 7.1 · IB 2.4

In 30 seconds

Good decisions compare the extra (marginal) benefit of one more unit with its extra (marginal) cost. Keep going while MB is at least MC, and stop where $ MB = MC $.
Costs include explicit costs (money you pay) and implicit costs (what you give up). Sunk costs, which you cannot get back, should be ignored.
Marginal utility falls as you consume more of a good. You get the most satisfaction from your budget when $ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} $ and all the money is spent.
Exam point: compare marginal utility per dollar, not marginal utility on its own. This rule, plus the income and substitution effects, explains why demand curves slope downwards.

Video lesson coming soonA short animated lesson for this step will appear here.

Cost-benefit thinking: what does a choice really cost?

Suppose you are deciding whether to spend Saturday working at a café for $60 or revising for a maths test. If you revise, you do not pay anything in cash. But revising is not free: you give up the $60 you could have earned. Economists count both kinds of cost.

Key termExplicit cost: a cost that involves an actual money payment, such as rent, wages or the price of a bus ticket.

Key termImplicit cost: the value of something you give up that does not involve a money payment, such as the wage you could have earned or the interest your savings could have made.

Economic cost = explicit + implicit costs. A $15 cinema ticket that also costs you two hours of work at $10 an hour has an economic cost of $ 15 + 20 = \$35 $.

Thinking at the margin: the MB = MC rule

Most choices are not “all or nothing”: you choose how many hours to revise. The useful question is “Is one more hour worth it?” That is thinking at the margin.

Total benefit (TB) is all the benefit you get from every unit together.
Marginal benefit (MB) is the extra benefit from one more unit: $ MB = \frac{\Delta TB}{\Delta Q} $.
Total cost (TC) is the cost of all the units together.
Marginal cost (MC) is the extra cost of one more unit: $ MC = \frac{\Delta TC}{\Delta Q} $.

Usually MB falls as you do more (the first hour helps most) and MC rises (each extra hour costs you something you value more, like sleep).

\[ \text{Optimal quantity: } MB = MC \]

If MB > MC, one more unit raises net benefit (TB − TC); if MB < MC, it lowers it. Stop at the last unit where MB is at least MC.

Worked example

Sara values each hour of revision as shown below. Find how many hours she should revise.

Hours	MB ($)	MC ($)	TB ($)	TC ($)	Net benefit ($)
1	20	4	20	4	16
2	16	8	36	12	24
3	12	10	48	22	26
4	8	14	56	36	20
5	4	20	60	56	4

Step 1Compare MB and MC hour by hour: hour 1 $ 20 > 4 $, hour 2 $ 16 > 8 $, hour 3 $ 12 > 10 $. All worth doing.

Step 2Hour 4: $ MB = 8 < MC = 14 $. This hour would reduce net benefit by $ 14 – 8 = \$6 $.

Step 3Check with totals: net benefit at 3 hours $ = 48 – 22 = \$26 $, the largest value in the table.

Sara should revise for 3 hours. The marginal and total methods always agree.

Ignore sunk costs

A sunk cost is money (or time) already spent that you cannot get back. If you paid $40 for a non-refundable concert ticket and feel ill on the night, the $40 is gone whether you go or not. Compare only the future benefits and costs. “I paid, so I must go” is the sunk cost fallacy.

Utility: total, marginal and diminishing

The benefit from buying something is the satisfaction it gives, called utility, measured in imaginary units called utils.

Key termMarginal utility (MU): the extra satisfaction from consuming one more unit of a good, $ MU = \frac{\Delta TU}{\Delta Q} $.

Think about slices of pizza when you are hungry. The first is wonderful; by the fifth you are barely enjoying it.

Slices	Total utility (TU)	Marginal utility (MU)
1	10	10
2	18	8
3	24	6
4	28	4
5	30	2
6	30	0
7	28	−2

MU falls with every slice: the law of diminishing marginal utility says each extra unit consumed in a period adds less satisfaction than the one before.
TU rises while MU is positive, peaks when $ MU = 0 $ (6 slices), then falls.

DiagramDraw two graphs, one above the other, with “Quantity” on both horizontal axes. Top: “Total utility” rises steeply, flattens, peaks at 6 slices and turns down. Bottom: “Marginal utility” is a downward-sloping line crossing the horizontal axis at 6, directly below the TU peak.

Spending a budget: the utility-maximising rule

Now add prices and a budget. A $2 coffee giving 20 utils is no better value than a $1 cookie giving 10 utils: both give 10 utils per dollar. So compare marginal utility per dollar.

\[ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} \quad \text{and} \quad P_x Q_x + P_y Q_y = \text{Income} \]

This is the utility-maximising rule. Cambridge calls it the equi-marginal principle: total utility is highest when the last dollar spent on each good gives the same extra utility. If $ \frac{MU_x}{P_x} > \frac{MU_y}{P_y} $, move spending from Y to X; as you buy more X its MU falls (and Y’s MU rises) until the ratios are equal.

Worked example

Omar has $10 to spend on coffees (X) at $2 each and cookies (Y) at $1 each. His marginal utilities are shown below. What should he buy?

Unit	MU of coffee	MU/P coffee	MU of cookies	MU/P cookies
1	20	10	12	12
2	16	8	10	10
3	12	6	8	8
4	8	4	6	6
5	4	2	4	4

Step 1Work out MU/P for each unit (done in the table: coffee MU ÷ 2, cookie MU ÷ 1).

Step 2Buy in order of highest MU per dollar: cookie 1 (12), then coffee 1 and cookie 2 (both 10), then coffee 2 and cookie 3 (both 8), then coffee 3 and cookie 4 (both 6).

Step 3Check the budget: $ 3 \times \$2 + 4 \times \$1 = \$6 + \$4 = \$10 $. All the money is spent.

Step 4Check the rule: $ \frac{MU_x}{P_x} = \frac{12}{2} = 6 $ and $ \frac{MU_y}{P_y} = \frac{6}{1} = 6 $. Equal.

Omar buys 3 coffees and 4 cookies. Total utility $ = (20 + 16 + 12) + (12 + 10 + 8 + 6) = 48 + 36 = 84 $ utils. Any other $10 combination gives less: for example, 4 coffees and 2 cookies gives $ 56 + 22 = 78 $.

Common mistakeChoosing the good with the higher MU, and forgetting price. The 3rd coffee (MU 12) looks better than the 4th cookie (MU 6), but per dollar they are equal. Also, never count a sunk cost as part of marginal cost.

From utility to the demand curve

The rule also explains the law of demand. Suppose the price of coffee falls from $2 to $1. Coffee’s MU per dollar doubles to 20, 16, 12, 8, 4. Repeating the steps with $10:

Buy in order of MU/P: coffee 1 (20), coffee 2 (16), coffee 3 and cookie 1 (12), cookie 2 (10), coffee 4 and cookie 3 (8), cookie 4 (6), coffee 5 and cookie 5 (4).
Spending: $ 5 \times \$1 + 5 \times \$1 = \$10 $. Check: $ \frac{4}{1} = \frac{4}{1} $.

When the price of coffee was $2 he bought 3; at $1 he buys 5. These are two points on his downward-sloping demand curve for coffee. Because of diminishing MU, he only buys extra units if the price falls.

Income and substitution effects

A price fall changes quantity demanded through two channels:

Substitution effect: the good is now cheaper compared with other goods, so you swap towards it. This always raises quantity demanded when price falls.
Income effect: a lower price raises your real income (what your money can buy). For a normal good this also raises quantity demanded; for an inferior good it works the other way, but the substitution effect is normally stronger.

Limitations of the utility model

Cambridge (and IB, through behavioural economics) asks you to evaluate this model.

Utility cannot be measured. Nobody can really say a coffee gives “20 utils”. The model shows the logic of choice, not real numbers.
People are not always rational. They buy on impulse, follow habits, copy friends, and are influenced by advertising and how choices are presented.
Information is limited. Consumers often do not know the quality of a product until after buying it, and do not have time to compare every option. Economists call this bounded rationality: people use rules of thumb instead of calculating.
Many goods are indivisible. You cannot buy half a car or a fraction of a phone, so ratios rarely become exactly equal.

A good evaluation says: the model gives a clear reason for downward-sloping demand and for “thinking at the margin”, but it assumes a level of calculation and information that real shoppers rarely have.

Exam tipAP Micro: multiple-choice questions often give MU and price tables. Divide MU by price first, then buy in order of MU per dollar until the budget runs out, and state the condition $ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} $. In an FRQ, if $ MU_x/P_x > MU_y/P_y $, the answer is “buy more X and less Y”, with the reason “the last dollar spent on X gives more additional utility”. Cambridge 9708: name the equi-marginal principle, link it to downward-sloping demand, then evaluate with at least two limitations. IB: link these to behavioural economics.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. Total utility from 1, 2, 3 and 4 smoothies is 15, 27, 36 and 42 utils. Calculate the marginal utility of each smoothie. Does this show diminishing marginal utility? Show worked answer

MU of 1st = 15
MU of 2nd = $ 27 – 15 = 12 $
MU of 3rd = $ 36 – 27 = 9 $
MU of 4th = $ 42 – 36 = 6 $
Yes. Each extra smoothie adds less satisfaction than the one before (15, 12, 9, 6), even though total utility is still rising.

EasyQ2. Ali leaves a job paying $25,000 a year to run his own bakery. In the first year he pays $40,000 for rent, flour and equipment. What are his explicit costs, implicit costs and total economic cost? Show worked answer

Explicit costs = $40,000 (money actually paid out).
Implicit cost = $25,000 (the salary he gave up).
Economic cost = $ 40{,}000 + 25{,}000 = \$65{,}000 $.

MediumQ3. A student is deciding how many tutoring sessions to take. The marginal benefit of sessions 1 to 5 is $50, $40, $30, $20 and $10. The marginal cost is $15, $20, $25, $30 and $35. How many sessions should she take, and what is her total net benefit? Show worked answer

Session 1: $ 50 > 15 $ ✓. Session 2: $ 40 > 20 $ ✓. Session 3: $ 30 > 25 $ ✓. Session 4: $ 20 < 30 $, so stop.
She should take 3 sessions.
Net benefit = $ (50 – 15) + (40 – 20) + (30 – 25) = 35 + 20 + 5 = \$60 $.

MediumQ4. A consumer spends all her income. For the last unit bought, good X has MU = 30 and price $3; good Y has MU = 20 and price $4. Is she maximising utility? If not, what should she do? Show worked answer

$ \frac{MU_x}{P_x} = \frac{30}{3} = 10 $ utils per dollar
$ \frac{MU_y}{P_y} = \frac{20}{4} = 5 $ utils per dollar
The ratios are not equal, so she is not maximising utility. The last dollar on X gives twice as much utility as the last dollar on Y. She should buy more X and less Y. As she does, MU of X falls and MU of Y rises until the ratios are equal.

MediumQ5. Good X costs $4 and good Y costs $2. A consumer with $20 buys 3 units of X and 4 units of Y. The MU of the 3rd unit of X is 24 and the MU of the 4th unit of Y is 12. Is this the utility-maximising choice? Show worked answer

Budget: $ 3 \times 4 + 4 \times 2 = 12 + 8 = \$20 $. All income is spent ✓.
$ \frac{24}{4} = 6 $ and $ \frac{12}{2} = 6 $. The ratios are equal ✓.
Both conditions hold, so yes, this combination maximises utility.

ExamQ6. Layla has $15 to spend on good A (price $3) and good B (price $2). The MU of units 1 to 5 of A is 30, 24, 18, 12, 6. The MU of units 1 to 5 of B is 20, 16, 12, 8, 4. (a) Find the utility-maximising combination and show it satisfies the rule. (b) Calculate total utility. (c) Explain, using the income and substitution effects, what would happen to the quantity of A if its price rose (assume A is a normal good). [8 marks] Show worked answer

(a) MU/P for A: 10, 8, 6, 4, 2. MU/P for B: 10, 8, 6, 4, 2. [1 mark]
Buy in order: A1 and B1 (10) cost $5; A2 and B2 (8) cost $5 more, total $10; A3 and B3 (6) cost $5 more, total $15. [1 mark]
Combination: 3 units of A and 3 units of B. Check: $ 3 \times 3 + 3 \times 2 = 9 + 6 = \$15 $ and $ \frac{18}{3} = \frac{12}{2} = 6 $. [2 marks]
(b) $ TU = (30 + 24 + 18) + (20 + 16 + 12) = 72 + 48 = 120 $ utils. [1 mark]
(c) A higher price lowers $ MU_A/P_A $, so A becomes worse value per dollar than B; Layla substitutes towards B (substitution effect). [1 mark] The higher price also lowers her real income, so she can afford less; for a normal good she buys less A (income effect). [1 mark] Both effects reduce the quantity of A demanded, which is a movement up her demand curve. [1 mark]

Check yourself

1. A consumer finds that $ MU_x/P_x = 8 $ and $ MU_y/P_y = 5 $. To raise total utility she should:

The last dollar on X gives more extra utility, so shift spending towards X until the ratios are equal.

2. You paid $30 for a non-refundable class but now have a better offer for the same time. The $30 should:

A sunk cost cannot be recovered whatever you choose, so it should not affect the decision.

3. Total utility is at its maximum when:

TU rises while MU is positive and falls once MU turns negative, so it peaks where MU = 0.

Your score: 0 out of 3

The short version

Economic cost = explicit costs + implicit costs. Ignore sunk costs; only future, avoidable costs matter.
Think at the margin: keep doing something while MB ≥ MC; the best quantity is where $ MB = MC $, which also gives the largest net benefit.
Marginal utility diminishes as you consume more; total utility peaks where MU = 0.
With a budget, maximise utility where $ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} $ and all income is spent (the equi-marginal principle).
A lower price raises MU per dollar, so people buy more: this, with the substitution and income effects, gives a downward-sloping demand curve. The model’s limits: utility is not measurable and people are not perfectly rational or informed.