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 firms and data are fictional. Only addition, subtraction and multiplication are needed, so a four-function calculator is enough.
Question 1 (multiple choice · foundation)
Ellery Mugs, a fictional pottery, sells mugs at the market price of $8 each and cannot change this price. The marginal cost of each mug it makes per hour is:
| Mug | 1st | 2nd | 3rd | 4th | 5th | 6th |
|---|---|---|---|---|---|---|
| MC ($) | 5 | 4 | 5 | 7 | 9 | 11 |
How many mugs per hour maximize profit?
- (A) 2
- (B) 4
- (C) 5
- (D) 6
Answer and explanation
Answer: (B). MR is $8 for every mug. Mugs 1 to 4 each have MC below $8, so each adds to profit. The 5th mug has MC = $9 > $8, so it would cut profit by $1. Check: revenue minus variable cost is $3, $7, $10, $11, $10 and $7 for 1 to 6 mugs, highest at 4.
- (A) picks the output where MC is lowest. The firm should keep going while MR is above MC, not stop at the cheapest unit.
- (C) includes the 5th mug, whose MC ($9) is above MR ($8).
- (D) maximizes revenue ($48), not profit. The 5th and 6th mugs cost more than they earn.
Question 2 (multiple choice · core)
At its current output, a firm’s marginal revenue is $20 and its marginal cost is $14. Its marginal cost is rising. To increase its profit, the firm should:
- (A) increase output, because the next unit adds more to revenue than to cost.
- (B) reduce output, because it is producing where MR is not equal to MC.
- (C) keep output the same, because MR > MC shows the firm is already making a profit.
- (D) keep output the same and raise its price until it equals MC.
Answer and explanation
Answer: (A). Each extra unit changes profit by MR − MC = $20 − $14 = $6 at the margin. The firm should expand until MR = MC.
- (B) knows that MR should equal MC but moves the wrong way. Cutting output would remove units that add $6 each to profit.
- (C) confuses MR > MC (about the next unit) with total profit being positive (about all units). It also ignores that profit can still rise.
- (D) mixes up price and MC. Setting price equal to MC is not the profit-maximizing rule, and a price-taking firm cannot change its price.
Question 3 (multiple choice · core)
Harlow Print Studio, a fictional shop, must lower the price of its art posters to sell more per day:
| Posters per day | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Price ($) | 22 | 20 | 18 | 16 | 14 | 12 |
| MC of that poster ($) | 6 | 7 | 9 | 11 | 13 | 15 |
Which output and price maximize the studio’s profit?
- (A) 3 posters at $18 each
- (B) 3 posters at $14 each
- (C) 5 posters at $14 each
- (D) 6 posters at $12 each
Answer and explanation
Answer: (A). TR is $22, $40, $54, $64, $70 and $72, so MR is $22, $18, $14, $10, $6 and $2. Posters 1 to 3 have MR above MC ($22 > $6, $18 > $7, $14 > $9). The 4th has MR = $10 < MC = $11. So the studio sells 3 posters and charges the price at that quantity, $18.
- (B) has the right quantity but uses the MR of the 3rd poster ($14) as the price. Customers pay the price in the price row.
- (C) keeps producing while price is above MC. That treats price as if it were MR. The 4th and 5th posters add less to revenue than they cost.
- (D) maximizes total revenue ($72), not profit. The 6th poster even has MR of only $2.
Question 4 (calculation · core)
Calloway Honey, a fictional producer, sells jars of honey at the market price of $14 each. Its fixed cost is $20 per day.
| Jars per day (Q) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Total cost (TC, $) | 20 | 28 | 34 | 41 | 50 | 61 | 74 | 89 |
(a) Calculate the MC of each jar. (b) Use MR and MC to find the profit-maximizing output. (c) Calculate the profit at that output, and confirm it is the highest. (d) The market price falls to $10. Find the new profit-maximizing output and the profit or loss.
Worked solution
(a) MC = change in TC: $8, $6, $7, $9, $11, $13, $15 for jars 1 to 7.
(b) MR = $14 for every jar. Jars 1 to 6 have MC below $14. The 7th jar has MC = $15 > $14. Output = 6 jars per day.
(c) TR = 14 × 6 = $84; TC = $74; profit = $10 per day. Profits at each output are −$20, −$14, −$6, $1, $6, $9, $10, $9, so 6 jars is the highest.
(d) MR = $10. Jars 1 to 4 have MC of $8, $6, $7 and $9, all below $10. The 5th jar has MC = $11 > $10. Output = 4 jars. TR = $40; TC = $50; result = −$10 (a loss). Check: 3 jars gives $30 − $41 = −$11 and 5 jars gives $50 − $61 = −$11, so 4 jars gives the smallest loss.
Suggested mark points (4): 1 for all seven MCs; 1 for 6 jars with the MR and MC comparison; 1 for profit of $10; 1 for 4 jars and a loss of $10.
Common error: stopping at the jar with the lowest MC. The test is MR ≥ MC.
Question 5 (graph · core)
Calloway Honey takes the market price, and its MC curve is U-shaped.
(a) Draw a correctly labelled graph showing Calloway’s MR curve at a price P₁ and its MC curve. Label the profit-maximizing quantity Q₁. (b) The market price rises to P₂. Show the new MR curve and label the new profit-maximizing quantity Q₂. (c) Separately, the rent on Calloway’s storage unit doubles. State what happens to the profit-maximizing quantity, and explain.
Model answer and suggested Marlbridge rubric
(a) Vertical axis: “Price, cost, revenue ($ per jar)”. Horizontal axis: “Quantity (jars per day)”. Draw a horizontal line at P₁ labelled MR₁ = P₁. Draw a U-shaped MC curve. Mark Q₁ where the rising part of MC crosses MR₁, with a dashed line down to the quantity axis.
(b) Draw a higher horizontal line at P₂, labelled MR₂ = P₂. It crosses the rising part of MC farther to the right, at Q₂ > Q₁. A higher price makes extra jars worth producing that were not worth it before.
(c) No change. Rent is a fixed cost. It does not change with output, so it does not change MC. MR and MC still cross at the same quantity. Calloway’s profit falls by the extra rent.
| Point | What earns it |
|---|---|
| 1 | Axes labelled; horizontal MR = P₁; U-shaped MC; Q₁ where rising MC crosses MR₁ |
| 1 | Higher MR₂ = P₂ with Q₂ to the right of Q₁ |
| 1 | Quantity unchanged after the rent rise |
| 1 | Reason: rent is a fixed cost, so MC (and MR) are unchanged; only profit falls |
Do not award the first point if Q₁ is placed where MC crosses MR on its falling part.
Question 6 (constructed response · core)
Kittiwake Boat Tours, a fictional company, runs boat tours. To sell more tours per day it must lower the price. Its fixed cost is $60 per day.
| Tours per day (Q) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Price ($) | 90 | 80 | 70 | 60 | 50 | 40 |
| MC of that tour ($) | 20 | 25 | 30 | 35 | 40 | 45 |
(a) Calculate total revenue and marginal revenue for each output. (b) Identify the profit-maximizing number of tours and the price. Explain using MR and MC. (c) Calculate the maximum daily profit. (d) The manager proposes running 5 tours a day “to maximize revenue”. Evaluate the proposal with numbers.
Model answer and suggested Marlbridge rubric
(a)
| Q | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| TR ($) | 90 | 160 | 210 | 240 | 250 | 240 |
| MR ($) | 90 | 70 | 50 | 30 | 10 | −10 |
(b) Tours 1 to 3 have MR above MC ($90 > $20, $70 > $25, $50 > $30), so each adds to profit. The 4th tour has MR = $30 < MC = $35, so it would cut profit by $5. 3 tours a day at $70 each.
(c) TC = $60 + $20 + $25 + $30 = $135. Profit = $210 − $135 = $75 per day.
(d) Revenue is highest at 5 tours ($250). But TC at 5 tours is $60 + $150 = $210, so profit is $250 − $210 = $40, which is $35 less than at 3 tours. The 4th and 5th tours each add more to cost than to revenue (MR of $30 and $10 against MC of $35 and $40). The proposal raises revenue but lowers profit, so it should be rejected if the goal is profit.
| Point | What earns it |
|---|---|
| 1 | Correct TR and MR rows |
| 1 | 3 tours, supported by MR ≥ MC up to the 3rd tour and MC > MR for the 4th |
| 1 | Price of $70 read from the price row (not $50 or $30) |
| 1 | Profit of $75 |
| 1 | Profit at 5 tours ($40) compared with $75, with the reason that MC > MR for the extra tours |
Accept the total approach in (b) if the full profit row is shown ($10, $55, $75, $70, $40, −$15), as long as the MR and MC comparison is also given.
Question 7 (explanation · stretch)
Use Calloway Honey from Question 4 (price $14, fixed cost $20, profit-maximizing output 6 jars).
(a) Explain, using marginal reasoning, why a firm producing where MC is greater than MR can raise its profit by producing less. (b) The city adds a fee of $2 on every jar sold, paid by the firm. Find the new profit-maximizing output and the profit or loss. (c) Instead of (b), the city charges a yearly licence fee that works out at $30 per day, whatever the output. Find the profit-maximizing output and the profit or loss. (d) Explain why the two policies have different effects on output.
Model answer and suggested Marlbridge rubric
(a) The last unit produced adds MC to cost but only MR to revenue. If MC > MR, that unit lowers profit by MC − MR. Cutting it out saves more cost than it loses in revenue, so profit rises. The firm should keep cutting until MR = MC.
(b) The fee raises every jar’s MC by $2: $10, $8, $9, $11, $13, $15, $17. Jars 1 to 5 have MC below $14; the 6th has MC = $15 > $14. New output = 5 jars. TC = $61 + $10 = $71; TR = $70; result = −$1 (a loss of $1). Check: 4 jars gives $56 − $58 = −$2 and 6 jars gives $84 − $86 = −$2.
(c) The licence is a fixed cost: it does not change MC. Output stays at 6 jars. Profit = $10 − $30 = −$20 (a loss of $20).
(d) A per-unit fee is a variable cost, so it raises MC. MC now crosses MR at a lower quantity, and output falls. A licence is a fixed cost. It raises total cost by the same amount at every output, so MC and the profit-maximizing output do not change; only profit falls.
| Point | What earns it |
|---|---|
| 1 | (a) MC > MR means the last unit lowers profit; producing less raises profit |
| 1 | (b) 5 jars, with the new MCs compared with $14 |
| 1 | (b) result of −$1 |
| 1 | (c) 6 jars and −$20 |
| 1 | (d) per-unit fee raises MC; licence is fixed, so MC and output are unchanged |
How did you do?
- Q1, Q2 or Q4 wrong: re-read “Marginal revenue and marginal cost” and Worked example 1 in the study guide. Keep producing while MR ≥ MC.
- Q3 or Q6 wrong: re-read Worked example 2. Use MR, not price, to choose the quantity; use the price row to set the price.
- Q5 marked down: check Figure 1 for where rising MC crosses MR, and label both axes.
- Q7 incomplete: re-read “Why fixed costs do not change the output”.
Then tick off the topic checklist.