Consumer Choice worksheet

Consumer Choice: answer key

1. 1. (C) The utility-maximizing rule is MU/P equal across all goods, not raw MU, not total utility, and definitely not equal dollar amounts. B ignores prices entirely, which is a problem because a good with sky-high marginal utility but a massive price tag might deliver terrible value per dollar. A confuses total with marginal utility, and total utility levels across different goods have nothing to do with the optimization condition.

2. 2. (B) Each additional unit gives you less satisfaction, so you'll only buy the next unit if the price drops enough to justify that lower marginal utility. That's a downward-sloping demand curve. A is about increasing marginal costs on the production side, which is a completely different concept on a different side of the market. C is about firm entry and exit in competitive markets, which has nothing to do with how individual consumers value successive units of a good.

3. 3. (B) Notebook price dropped, so the maximum number of notebooks the student can afford jumps from 5 to 10. Maximum pens stays at 10 (pen price didn't change). The budget line pivots outward along the notebook axis. One endpoint moves and the other doesn't. A would require an income change with both prices held constant; that gives a parallel shift. D is wrong because a price change alters your real purchasing power even when your nominal income stays the same.

4. 4. (B) Do the math. MU_X / P_X = 30/5 = 6 utils per dollar. MU_Y / P_Y = 20/10 = 2 utils per dollar. X gives triple the satisfaction per dollar, so shift spending from Y toward X. As you buy more X, diminishing marginal utility drags MU_X down; as you buy less Y, MU_Y rises. Eventually the ratios converge and you're at equilibrium. D is wrong because 6 doesn't equal 2 and the current allocation is clearly leaving satisfaction on the table.

5. 5. (A) For normal goods, the two effects reinforce each other. Substitution effect: the good is relatively cheaper, so you buy more of it. Income effect: the price drop effectively raised your real income, and for a normal good you buy more when income rises. Both push quantity demanded upward. C and D describe what happens with inferior goods, where the income effect works against the substitution effect.

6. 6. (B) The substitution effect isolates the price-ratio change while holding real income constant. Good A got cheaper relative to Good B, so you substitute toward A. That's it. A describes the income effect. The feeling-wealthier part is about purchasing power, not relative prices. C is wrong because a change in a good's own price causes movement along the demand curve, not a shift of the whole curve.

7. 7. (A) If the 5th unit adds zero satisfaction, then total utility peaked at 4 units. The 5th unit doesn't help and consuming a 6th would actually reduce total utility (negative marginal utility). C confuses marginal with total; total utility is the sum of all marginal utilities from units 1 through 4, which is definitely positive. B is wrong because the 5th unit contributes nothing, so unless it's free there's no reason to buy it. Stopping at 4 is optimal.

8. 8. (B) The price drop raises real income. By definition, when income goes up consumers buy less of inferior goods, so the income effect alone pushes quantity down. The substitution effect still pushes quantity up (the good is relatively cheaper). For most inferior goods the substitution effect wins overall and quantity still increases on net. But the question asks specifically about the income effect in isolation, and that component reduces purchases. A describes the income effect for a normal good, not an inferior one.

9. 9. (B) MU_A / P_A = 18/3 = 6 utils per dollar. MU_B / P_B = 30/6 = 5 utils per dollar. A delivers more satisfaction per dollar, so shift spending from B toward A until the ratios converge. The classic trap is A, which compares raw MU (30 > 18) instead of MU per dollar (5 < 6). Higher marginal utility doesn't mean better value if the price is proportionally higher. C is wrong because positive marginal utility from both goods doesn't mean the allocation is optimal; the unequal MU/P ratios prove you could do better by reshuffling.

10. 10. (C) Marginal utility = change in total utility from one more unit. For the 3rd slice: 46 - 36 = 10 utils. A (46) is the total utility after three slices, not the marginal gain from the third one. B (15.3) comes from dividing total utility by quantity (46/3), which gives you average utility, a different concept entirely. D (4 utils) is the marginal utility of the 4th slice (50 - 46), not the 3rd.

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