These are original Marlbridge practice questions, not past exam questions. The mark points are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. All people, prices and utility values are fictional. Only addition, subtraction and division are needed, so a four-function calculator is enough.
Questions 4 and 5 use the same data. Leena hires a kayak at a fictional lake. Each hour costs $12. Her marginal benefit from each hour, valued in dollars, is:
| Hour | 1st | 2nd | 3rd | 4th | 5th | 6th |
|---|---|---|---|---|---|---|
| MB ($) | 30 | 25 | 19 | 14 | 10 | 5 |
Questions 6 and 7 use the same data. Omar spends his pocket money on juice and samosas. His marginal utilities are:
| Unit | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| MU of juice (utils) | 24 | 20 | 14 | 10 | 5 | – | – |
| MU of samosas (utils) | 15 | 12 | 10 | 7 | 5 | 3 | 2 |
Question 1 (multiple choice · foundation)
Mei’s total utility from cups of tea in one day is 12, 22, 30, 35 and 37 utils for 1 to 5 cups. What is the marginal utility of the 3rd cup?
- (A) 8 utils
- (B) 30 utils
- (C) 10 utils
- (D) 5 utils
Answer and explanation
Answer: (A). MU of the 3rd cup = TU at 3 cups − TU at 2 cups = 30 − 22 = 8 utils.
- (B) is the total utility of 3 cups, not the extra utility of the 3rd.
- (C) is the average utility of 3 cups, 30 ÷ 3 (it is also the MU of the 2nd cup, 22 − 12). Neither is the extra utility of the 3rd cup.
- (D) is the MU of the 4th cup (35 − 30).
Question 2 (multiple choice · core)
Nadia paid a non-refundable $40 for a day pass to a fictional theme park. Inside, each ride costs an extra $5 token. After three rides, she values a 4th ride at $6. What should a rational Nadia do?
- (A) Take the 4th ride, because its marginal benefit ($6) is greater than its marginal cost ($5).
- (B) Not take the 4th ride, because she has already spent more than $40 today.
- (C) Keep taking rides until her total benefit for the day is at least $40, whatever each ride is worth.
- (D) Not take the 4th ride, because marginal benefit is falling.
Answer and explanation
Answer: (A). The decision is about one more ride, so compare its MB ($6) with its MC ($5). The ride adds $1 of net benefit. The $40 pass is sunk and is the same whatever she does next.
- (B) lets the sunk $40 drive the decision. What she has already spent cannot be recovered.
- (C) is the sunk cost fallacy: “getting her money’s worth” could mean taking rides whose MB is below $5, which lowers net benefit.
- (D) confuses a falling MB with an MB below MC. MB can fall and still be above MC.
Question 3 (multiple choice · core)
Jo spends all her income on books ($5 each) and cinema tickets ($8 each). For the last units she bought, the marginal utility of a book is 50 utils and of a ticket is 64 utils. To increase her total utility, Jo should:
- (A) buy more books and fewer tickets.
- (B) buy more tickets and fewer books.
- (C) change nothing, because she already spends all her income.
- (D) buy more of both goods.
Answer and explanation
Answer: (A). MU per dollar: books 50 ÷ 5 = 10 utils per $; tickets 64 ÷ 8 = 8 utils per $. A dollar moved from tickets to books gains about 10 utils and loses about 8. As she buys more books and fewer tickets, the book ratio falls and the ticket ratio rises until they are equal.
- (B) compares MU (64 > 50) and ignores the prices.
- (C) checks only one of the two conditions. Spending all income is necessary, but the ratios must also be equal.
- (D) is not affordable: she already spends all her income.
Question 4 (calculation · core)
Use Leena’s kayak data.
(a) Identify the number of hours Leena should hire, and explain using marginal analysis. (b) Calculate her total net benefit at that number of hours, and show that one more hour would lower it. (c) The lake also charges a non-refundable $15 booking fee, paid when she arrives. Does this change your answer to (a)? Explain.
Worked solution
(a) MC = $12 per hour. Hours 1 to 4 have MB ($30, $25, $19, $14) greater than $12, so each adds to net benefit. The 5th hour has MB $10 < $12, so it would lower net benefit. Leena should hire 4 hours.
(b) Total benefit for 4 hours = 30 + 25 + 19 + 14 = $88. Total cost = 4 × $12 = $48. Total net benefit = 88 − 48 = $40. A 5th hour adds $10 of benefit and $12 of cost, so net benefit falls by $2 to $38 (check: 98 − 60 = 38).
(c) No. The $15 fee is sunk once paid. It is the same at every number of hours, so it does not change the MB or MC of any hour. She still hires 4 hours. Her net gain falls to $40 − $15 = $25.
Suggested mark points (3): 1 for 4 hours with an MB-versus-MC comparison on both sides (14 > 12 and 10 < 12); 1 for $40 and $38 (or “falls by $2”); 1 for “no change” because the fee does not affect MB or MC.
Common error: stopping at 3 hours because MB “falls a lot” after that. The 4th hour still adds $14 − $12 = $2.
Question 5 (graph · core)
Use Leena’s kayak data.
(a) Draw a correctly labelled graph showing Leena’s marginal benefit and her marginal cost of $12 per hour. Label the optimal number of hours. (b) The price rises to $20 per hour. Show the change on your graph and identify the new optimal number of hours. (c) Use your graph to explain why hiring a 3rd hour at $20 would make Leena worse off.
Model answer and suggested Marlbridge rubric
(a) Horizontal axis: “Hours of kayak hire”. Vertical axis: “Dollars per hour”. Plot MB at (1, 30), (2, 25), (3, 19), (4, 14), (5, 10), (6, 5) and join the points: a downward-sloping line labelled MB. Draw a horizontal line at $12 labelled MC₁. MB is above MC₁ up to hour 4 and below it from hour 5, so label 4 hours as the optimum.
(b) Draw a new horizontal line at $20 labelled MC₂, above MC₁. MB is above $20 for hours 1 and 2 ($30 and $25) and below it for hour 3 ($19). The new optimum is 2 hours.
(c) At hour 3, the MB point ($19) lies below the MC₂ line ($20). That hour would add $19 of benefit but $20 of cost, so total net benefit would fall by $1 (from $15 at 2 hours to $14 at 3 hours).
| Point | What earns it |
|---|---|
| 1 | Both axes labelled; MB downward sloping through the data; MC₁ horizontal at $12 |
| 1 | Optimum of 4 hours shown, consistent with the graph |
| 1 | MC₂ drawn above MC₁ and new optimum of 2 hours identified |
| 1 | Hour 3 explained: MB ($19) < MC ($20), so net benefit falls |
Accept a step graph or bars for MB if each hour’s value is clear.
Question 6 (constructed response · core)
Use Omar’s utility table. Omar has $10 to spend. Juice costs $2 and samosas cost $1.
(a) Calculate the marginal utility per dollar for each unit of juice and each samosa. (b) Identify the combination of juice and samosas that maximizes Omar’s total utility, and show that it meets both conditions for utility maximization. (c) Calculate his total utility at that combination. (d) Omar’s friend suggests 2 juices and 6 samosas, which also costs $10. Explain, using marginal utility per dollar, why this is not the best choice.
Model answer and suggested Marlbridge rubric
(a) Juice (÷ $2): 12, 10, 7, 5, 2.5. Samosas (÷ $1): 15, 12, 10, 7, 5, 3, 2.
(b) 3 juices and 4 samosas. Spending: 3 × $2 + 4 × $1 = $6 + $4 = $10, all his income. Last units: juice 14 ÷ 2 = 7 and samosa 7 ÷ 1 = 7 utils per dollar, so the ratios are equal.
(c) Total utility = (24 + 20 + 14) + (15 + 12 + 10 + 7) = 58 + 44 = 102 utils.
(d) With 2 juices and 6 samosas, the last samosa gives only 3 utils per dollar, but a 3rd juice would give 7 utils per dollar. Moving $2 from samosas to juice raises utility. Total utility is 44 + 52 = 96 utils, less than 102.
| Point | What earns it |
|---|---|
| 1 | MU per dollar correct for both goods |
| 1 | 3 juices and 4 samosas, with spending of $10 shown |
| 1 | Equal ratios (7 = 7) for the last unit of each good |
| 1 | 102 utils |
| 1 | (d) compares the last samosa’s MU per dollar (3) with the next juice’s (7) and concludes spending should move to juice |
Do not award the third point for comparing MU (14 and 7) instead of MU per dollar.
Question 7 (explanation · stretch)
(a) State two assumptions of the model of rational consumer choice. (b) The price of juice falls from $2 to $1. Omar still has $10, and his marginal utilities are unchanged. Show that his old combination (3 juices, 4 samosas) no longer maximizes utility. (c) Find his new utility-maximizing combination and his total utility. (d) What does your answer suggest about the link between the price of a good and the quantity a consumer buys?
Model answer and suggested Marlbridge rubric
(a) Any two: consumers have limited income and face given prices; consumers are rational and choose to maximize total utility; preferences are known and consistent; marginal utility diminishes as more of a good is consumed.
(b) At the new prices the old combination costs 3 × $1 + 4 × $1 = $7, so $3 is unspent: the budget condition fails. Also, the next juice gives 10 ÷ 1 = 10 utils per dollar, more than the next samosa’s 5 ÷ 1 = 5, so juice is now the better use of extra money.
(c) Both goods now cost $1, so MU per dollar equals MU. 5 juices and 5 samosas: spending 5 × $1 + 5 × $1 = $10; last units 5 ÷ 1 = 5 and 5 ÷ 1 = 5, equal. Total utility = (24 + 20 + 14 + 10 + 5) + (15 + 12 + 10 + 7 + 5) = 73 + 49 = 122 utils.
(d) When the price of juice fell, Omar’s quantity of juice rose from 3 to 5. A lower price raises the MU per dollar of the good, so a utility-maximizing consumer buys more of it. This is one reason demand curves slope downward, which you will meet in Unit 2.
| Point | What earns it |
|---|---|
| 1 | Two valid assumptions |
| 1 | Old combination fails: money left over or unequal ratios (10 > 5), with numbers |
| 1 | 5 juices and 5 samosas, with $10 spent and equal ratios shown |
| 1 | 122 utils |
| 1 | Lower price leads to more juice bought, linked to a higher MU per dollar |
How did you do?
- Q1 wrong: re-read “Total utility and marginal utility” in the study guide. MU is a change, not a total or an average.
- Q2 or Q4(c) wrong: re-read “Sunk costs do not change the best quantity”.
- Q4 or Q5 wrong: re-read “Thinking at the margin” and Worked example 1, and compare your graph with Figure 2.
- Q3, Q6 or Q7 wrong: re-read “Spending a budget on two goods” and Worked example 2. Always divide MU by price.
Then tick off the topic checklist.