Consumer Choice & Utility Maximization

You’ll be able to

State the law of diminishing marginal utility and its effect on demand
Apply the utility-maximizing rule that equalizes marginal utility per dollar
Explain how a price change redirects spending toward the cheaper good

Utility falls as consumption rises

Utility is satisfaction; marginal utility is the satisfaction from one more unit. The law of diminishing marginal utility says that each additional unit of the same good delivers less added satisfaction than the last. The first glass of water on a hot day is worth a great deal, the fourth very little. This is not a psychological curiosity — it is the reason demand curves slope downward. A consumer will only buy more of something if its price falls, because the extra units are worth less to them.

The utility-maximizing rule

MU_x / P_x = MU_y / P_y (subject to spending the whole budget)

Equalize the satisfaction bought per dollar. Not MU_x = MU_y — a good that costs three times as much must deliver three times the utility to be worth the same.

Per dollar, not per unit

The optimum equalizes marginal utility per dollar, not marginal utility. If good X yields 30 utils and costs $3 while good Y yields 40 utils and costs $8, then X delivers 10 utils per dollar and Y delivers 5 — so despite Y being more satisfying per unit, the consumer should shift spending toward X. Buying more X drives its marginal utility down and buying less Y drives Y's up, and the shifting continues until the two ratios meet.

How this generates the demand curve

Start at an optimum and cut the price of X. The ratio MU_x/P_x rises immediately, because the denominator fell — so X is now the better buy and the consumer purchases more of it. That is the demand relationship: a lower price leads to a larger quantity demanded, derived rather than assumed. It also splits into two forces the exam names separately. The substitution effect is the shift toward X because it is now relatively cheaper. The income effect is the extra purchasing power freed up by the lower price, which can be spent on anything.

Worked example

A consumer with $24 chooses between burritos ($6, marginal utilities 60, 48, 36, 24) and coffees ($2, marginal utilities 20, 16, 12, 8). Find the utility-maximizing bundle.

1.Convert to utility per dollar. Burritos: 10, 8, 6, 4. Coffees: 10, 8, 6, 4.
2.Buy in descending order of utility per dollar: burrito 1 and coffee 1 both give 10.
3.Next, burrito 2 and coffee 2 both give 8. Then burrito 3 and coffee 3 both give 6.
4.Running cost: 3 burritos ($18) + 3 coffees ($6) = $24 — the budget is exactly spent.
5.Check the rule: the last burrito and the last coffee each deliver 6 utils per dollar. Equalized.

Answer: 3 burritos and 3 coffees. The equal utility-per-dollar at the margin, together with the fully spent budget, is what confirms the optimum — either condition alone is not enough.

Watch out

Two conditions must hold at the optimum: the ratios are equal AND the entire budget is spent. A bundle with equal ratios and money left over is not optimal — the leftover dollars could still buy utility.

Checkpoint

Good A gives 40 utils and costs $4; good B gives 30 utils and costs $2. A consumer maximizing utility should:

Checkpoint

The law of diminishing marginal utility helps explain why:

Checkpoint

A consumer is at an optimum when the price of good X falls. The immediate effect is that:

On the exam

Utility tables on the exam are almost always built so that a clean bundle exactly exhausts the budget. If your answer leaves money unspent or overspends, recheck the per-dollar column before doubting the arithmetic.

Answer the 3 checkpoints as you read.