How does a consumer with a fixed budget choose the combination of goods that gives the most satisfaction?
Topic 1.6 Marginal Analysis and Consumer Choice: explain diminishing marginal utility, and use the utility-maximizing rule (equal marginal utility per dollar) to find the consumption bundle that maximizes total utility given a budget.
A focused answer to AP Microeconomics Topic 1.6, covering total and marginal utility, the law of diminishing marginal utility, and the utility-maximizing rule that equalises marginal utility per dollar across goods, with worked exam-style questions.
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What this topic is asking
Topic 1.6 applies marginal analysis to the consumer: given a fixed budget and the prices of goods, how does a rational consumer choose the bundle that gives the most satisfaction? The College Board wants you to explain total and marginal utility, state the law of diminishing marginal utility, and apply the utility-maximizing rule that equalises the marginal utility per dollar across goods. This is the foundation of the demand curve you meet in Unit 2.
Total and marginal utility
Marginal utility is the change in total utility from one extra unit. As long as marginal utility is positive, total utility is still rising; total utility is maximized at the quantity where marginal utility reaches zero (one more unit would add nothing). For the consumer-choice problem, though, the budget usually binds long before that point, so the consumer stops well before marginal utility hits zero.
The law of diminishing marginal utility
Diminishing marginal utility is why a consumer does not spend the entire budget on a single good, and it is the deep reason demand curves slope downward: because each extra unit is worth less, a consumer will buy more only at a lower price. It also drives the reallocation logic of the utility-maximizing rule below, because spending more on a good pushes its marginal utility down, eventually equalising the per-dollar utilities across goods.
The utility-maximizing rule
The central result of the topic is a single condition.
The intuition is a reallocation argument. If one good currently delivers more utility per dollar than another, the consumer can raise total utility by moving a dollar from the lower-per-dollar good to the higher-per-dollar one. As they buy more of the higher one, its marginal utility falls (diminishing marginal utility), and the gap closes. The consumer stops reallocating when the per-dollar utilities are equal, because then no shift can raise total utility. Two conditions must both hold: the per-dollar utilities are equal and the entire budget is spent.
Try this
Q1. State the law of diminishing marginal utility. [1 point]
- Cue. As more units of a good are consumed in a period, the marginal utility of each additional unit eventually falls.
Q2. Good A gives 30 utils and costs 2. State which delivers more utility per dollar. [1 point]
- Cue. A gives 30/3 = 10 utils per dollar; B gives 16/2 = 8. Good A delivers more utility per dollar, so the consumer should buy more of A.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2017 (style)1 marksMultiple choice. A utility-maximizing consumer allocates a fixed budget so that (A) total utility from each good is equal. (B) the price of each good is equal. (C) the marginal utility of each good is equal. (D) the marginal utility per dollar spent is equal across all goods. (E) all income is spent on the cheapest good.Show worked answer →
The answer is (D). Utility is maximized when the marginal utility per dollar (marginal utility divided by price) is equal across all goods and the budget is fully spent.
(A) and (C) ignore prices; a high-utility good may also be expensive. (B) is irrelevant to the rule. (E) ignores diminishing marginal utility, which makes spending everything on one good suboptimal.
AP 2020 (style)4 marksFree response. A consumer with 2) and good Y (price $3). The marginal utilities of successive units of X are 20, 16, 12, 8 and of Y are 18, 15, 9, 6. (a) Define the law of diminishing marginal utility. (b) Calculate the marginal utility per dollar of the first unit of each good. (c) Determine the utility-maximizing bundle. (d) Explain why this bundle maximizes utility.Show worked answer →
A four-point consumer-choice FRQ.
(a) (1 point): as a consumer consumes more units of a good in a period, the marginal utility of each additional unit eventually falls.
(b) (1 point): first unit of X = 20 / 3 = 6 utils per dollar.
(c) (1 point): buying by best utility-per-dollar within the 6) and 2 units of Y (12.
(d) (1 point): at this bundle the marginal utility per dollar is equalised (X3 = 12/2 = 6 and Y2 = 15/3 = 5 are the last affordable purchases, with no reallocation able to raise total utility), and the whole budget is spent.
Related dot points
- Topic 1.1 Scarcity: explain how scarcity forces individuals and societies to make choices, distinguish needs from wants, identify the factors of production, and explain why every choice involves a trade-off.
A focused answer to AP Microeconomics Topic 1.1, covering scarcity, the economic problem, the four factors of production and their payments, the trade-offs scarcity forces, and how scarcity underpins every later micro model, with worked exam-style questions.
- Topic 1.5 Cost-Benefit Analysis: explain rational decision-making by comparing marginal benefit and marginal cost, distinguish explicit from implicit costs, and find the optimal quantity where marginal benefit equals marginal cost.
A focused answer to AP Microeconomics Topic 1.5, covering rational decision-making, marginal benefit versus marginal cost, explicit versus implicit costs, sunk costs, and finding the optimal quantity where marginal benefit equals marginal cost, with worked exam-style questions.
- Topic 1.3 The Production Possibilities Curve: draw and interpret the PPC, calculate opportunity cost from it, explain its shape in terms of constant versus increasing opportunity cost, and show efficiency, unattainable points, and growth.
A focused answer to AP Microeconomics Topic 1.3, covering how to draw and read the production possibilities curve, calculate opportunity cost, interpret straight-line versus bowed-out curves, and show efficiency, inefficiency, unattainable points, and economic growth, with worked exam-style questions.
- Topic 2.1 Demand: state the law of demand, distinguish a change in quantity demanded from a change in demand, and identify the determinants that shift the demand curve.
A focused answer to AP Microeconomics Topic 2.1, covering the law of demand, the difference between a movement along and a shift of the demand curve, the determinants of demand, and the income and substitution effects, with worked exam-style questions.
- Topic 2.3 Price Elasticity of Demand: calculate price elasticity of demand using the midpoint formula, classify demand as elastic, inelastic, or unit elastic, apply the total revenue test, and identify the determinants of elasticity.
A focused answer to AP Microeconomics Topic 2.3, covering the price elasticity of demand, the midpoint formula, elastic versus inelastic versus unit elastic demand, the total revenue test, perfectly elastic and inelastic cases, and the determinants of elasticity, with worked exam-style questions.
Sources & how we know this
- AP Microeconomics Course and Exam Description — College Board (2023)