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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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  1. What this topic is asking
  2. Total and marginal utility
  3. The law of diminishing marginal utility
  4. The utility-maximizing rule
  5. Try this

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 3;goodBgives16utilsandcosts3; good B gives 16 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.
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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 12buysgoodX(price12 buys good X (price 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.
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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 / 2=10utilsperdollar;firstunitofY=18/2 = 10 utils per dollar; first unit of Y = 18 / 3 = 6 utils per dollar.

(c) (1 point): buying by best utility-per-dollar within the 12budgetgivesX1(10),X2(16/2=8),Y1(6),X3(12/2=6),Y2(15/3=5)...theaffordablemaximisingbundleis3unitsofX(12 budget gives X1 (10), X2 (16/2=8), Y1 (6), X3 (12/2=6), Y2 (15/3=5)... the affordable maximising bundle is 3 units of X (6) and 2 units of Y (6),spendingexactly6), spending exactly 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.

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