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. A four-function calculator is enough. Give averages to 2 decimal places unless they are exact.
Questions 1 and 3 use Corvane Print Shop, a fictional firm with one printing press (fixed) that hires workers to print posters:
| Workers | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Total product (posters per hour) | 0 | 20 | 50 | 90 | 124 | 150 | 162 | 160 |
Question 1 (multiple choice · foundation)
What is the marginal product of the fifth worker at Corvane Print Shop?
- (A) 30 posters per hour
- (B) 31 posters per hour
- (C) 26 posters per hour
- (D) 150 posters per hour
Answer and explanation
Answer: (C). The fifth worker raises output from 124 to 150 posters, so MP = 150 − 124 = 26 posters per hour.
- (A) is the average product of 5 workers (150 ÷ 5). It divides instead of finding the change.
- (B) is the average product of 4 workers (124 ÷ 4).
- (D) is total product with 5 workers, a level rather than a change.
Question 2 (multiple choice · foundation)
Which statement best describes the short run for a firm?
- (A) Any period shorter than one year.
- (B) A period in which the firm can change all of its inputs.
- (C) A period in which the firm cannot change its output.
- (D) A period in which at least one of the firm’s inputs cannot be changed.
Answer and explanation
Answer: (D). The short run is defined by a fixed input, usually capital such as buildings or machines.
- (A) uses the calendar. The short run can be a week for a market stall and years for a power station.
- (B) describes the long run, when every input is variable.
- (C) is wrong because a firm can change output in the short run by changing its variable inputs, such as hiring more workers.
Question 3 (multiple choice · core)
At Corvane Print Shop, with which worker do diminishing marginal returns begin?
- (A) The 3rd worker
- (B) The 4th worker
- (C) The 5th worker
- (D) The 7th worker
Answer and explanation
Answer: (B). The marginal products are 20, 30, 40, 34, 26, 12 and −2. MP rises up to the third worker (40) and first falls with the fourth worker (34). Diminishing marginal returns begin where MP starts to fall.
- (A) is the worker with the highest MP. Returns are still increasing there.
- (C) is where average product starts to fall (from 31 to 30), because the fifth worker’s MP of 26 is below the average of 31. That is a different turning point.
- (D) is where MP becomes negative and TP falls (162 to 160). Diminishing returns began long before.
Question 4 (calculation · core)
Linden Laundry is a fictional firm with a fixed number of washing machines. The table shows the average product of labour, in shirts cleaned per hour.
| Workers | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Average product (shirts per worker per hour) | 30 | 35 | 36 | 33 | 30 | 26 |
(a) Calculate total product for 1 to 6 workers. (b) Calculate the marginal product of each worker. (c) Identify the worker with whom diminishing marginal returns begin. (d) The third worker’s marginal product is lower than the second worker’s, yet average product rises when the third worker is hired. Explain why.
Worked solution
(a) TP = AP × L: 30 × 1 = 30; 35 × 2 = 70; 36 × 3 = 108; 33 × 4 = 132; 30 × 5 = 150; 26 × 6 = 156 shirts per hour.
(b) MP = change in TP: first worker 30 − 0 = 30; second 70 − 30 = 40; third 108 − 70 = 38; fourth 132 − 108 = 24; fifth 150 − 132 = 18; sixth 156 − 150 = 6 shirts per hour.
(c) MP rises from 30 to 40, then falls to 38. Diminishing marginal returns begin with the third worker.
(d) The third worker adds 38 shirts. That is less than the second worker’s 40, but more than the current average of 35. When the marginal value is above the average, it pulls the average up: 108 ÷ 3 = 36 > 35. AP falls only from the fourth worker, whose MP of 24 is below the average of 36.
Suggested mark points (4): 1 for all six TP values; 1 for all six MP values; 1 for the third worker; 1 for comparing the third worker’s MP (38) with the existing AP (35), not with the previous MP.
Common error: dividing AP by L to get TP. Check: TP must be larger than AP once there is more than one worker.
Question 5 (graph · core)
A firm uses a fixed amount of capital and a variable amount of labour. Its marginal product of labour first rises, then falls, and eventually becomes negative.
(a) On one set of axes, sketch a correctly labelled total product curve. (b) On a second set of axes directly below, sketch correctly labelled marginal product and average product curves. (c) Mark on your graphs: (i) the quantity of labour where diminishing marginal returns begin, (ii) the quantity of labour where TP is at its maximum. (d) Explain why the MP curve must cross the AP curve at the highest point of AP.
Model answer and suggested Marlbridge rubric
(a) Horizontal axis: “Quantity of labour (workers)”. Vertical axis: “Total product (units of output)”. TP starts at the origin, gets steeper at first, then gets flatter, reaches a peak and turns down.
(b) Same horizontal axis, aligned with the top graph. Vertical axis: “Output per worker” or “MP, AP (units of output)”. MP rises to a peak and then falls, crossing the horizontal axis and becoming negative. AP rises and then falls more gently and stays positive. MP is above AP while AP rises, cuts AP at its peak from above, and is below AP after that.
(c) (i) Diminishing marginal returns begin at the labour quantity where MP is at its maximum. On the TP graph this is where TP stops getting steeper and starts getting flatter. (ii) TP is at its maximum at the labour quantity where MP = 0 (MP crosses the horizontal axis), directly below the peak of TP.
(d) AP is an average of the marginal products so far. If the next worker’s MP is above the current AP, it pulls the average up; if it is below, it pulls the average down. So AP rises while MP > AP and falls while MP < AP. AP must therefore reach its highest point exactly where MP = AP, which is where the curves cross.
| Point | What earns it |
|---|---|
| 1 | Both graphs have labelled axes (labour horizontally; output vertically) and labelled curves |
| 1 | TP gets steeper, then flatter, then falls, with its peak directly above MP = 0 |
| 1 | MP rises then falls below zero; AP rises then falls and stays positive; MP cuts AP at the maximum of AP |
| 1 | Diminishing returns marked at the maximum of MP |
| 1 | Explanation that MP above AP raises AP and MP below AP lowers it |
Do not award the third point if MP crosses AP to the right or left of AP’s peak.
Question 6 (constructed response · core)
Brewhaven is a fictional café. The table shows coffees made per hour with one espresso machine and, later, with two machines.
| Baristas | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| TP with one machine (coffees per hour) | 0 | 40 | 70 | 90 | 100 |
| TP with two machines (coffees per hour) | 0 | 45 | 90 | 125 | 150 |
(a) Calculate the marginal product of the third barista with one machine and with two machines. (b) With one machine, explain why each extra barista adds fewer coffees than the one before. (c) Is buying the second machine a short-run or a long-run decision? Explain, and state what happens to the total product curve. (d) The manager says: “Our marginal product falls because we keep hiring worse baristas.” Evaluate this claim.
Model answer and suggested Marlbridge rubric
(a) One machine: 90 − 70 = 20 coffees per hour. Two machines: 125 − 90 = 35 coffees per hour.
(b) The espresso machine is a fixed input in the short run. Each extra barista has to share the same machine, so baristas spend more time waiting to use it. Each one adds less to output than the one before (MP: 40, 30, 20, 10). This is diminishing marginal returns.
(c) It is a long-run decision: the café changes an input that was fixed. After it, there is a new short run with two machines fixed. The TP curve shifts up: every number of baristas makes more coffee (for example 4 baristas: 100 → 150).
(d) The claim is not supported by the model. Diminishing marginal returns would happen even if every barista were equally skilled, because each additional barista has a smaller share of the fixed machine. The evidence: with two machines, the third barista’s MP rises from 20 to 35 coffees. The same barista becomes more productive when the fixed input increases, so the cause was the machine, not the worker.
| Point | What earns it |
|---|---|
| 1 | Both MPs correct: 20 and 35 |
| 1 | Falling MP linked to sharing a fixed input |
| 1 | Long run, because a previously fixed input changes; TP shifts up |
| 1 | Rejects the claim, with the fixed-input reason or the evidence from (a) |
Question 7 (explanation · stretch)
Fenwick Tools, a fictional workshop, employs 5 workers. Their average product is 40 tools per day.
(a) Calculate total product with 5 workers. (b) A sixth worker is hired. Calculate the new average product if the sixth worker’s marginal product is (i) 28 tools per day, (ii) 46 tools per day. (c) Use your answers to state the rule that links marginal product and average product. (d) Suppose instead the sixth worker’s marginal product is −6 tools per day. Find the new total and average product, and explain why AP is still positive.
Model answer and suggested Marlbridge rubric
(a) TP = AP × L = 40 × 5 = 200 tools per day.
(b) (i) New TP = 200 + 28 = 228; AP = 228 ÷ 6 = 38 tools per worker per day. (ii) New TP = 200 + 46 = 246; AP = 246 ÷ 6 = 41 tools per worker per day.
(c) When MP is below AP (28 < 40), AP falls (to 38). When MP is above AP (46 > 40), AP rises (to 41). (If MP equalled 40, AP would stay at 40, which is why MP crosses AP at AP’s maximum.)
(d) TP = 200 − 6 = 194 tools per day; AP = 194 ÷ 6 = 32.33 tools per worker per day. TP falls because MP is negative: the workshop is so crowded that the sixth worker gets in the way. AP stays positive because it is total output (still 194) shared among workers. AP becomes zero or negative only if total output does.
| Point | What earns it |
|---|---|
| 1 | TP = 200 |
| 1 | Both new APs correct (38 and 41) with working |
| 1 | Rule stated in terms of MP above or below AP |
| 1 | TP 194 and AP 32.33, with the reason AP stays positive |
Accept an AP of 32.3 in (d) if the method is shown.
How did you do?
- Q1 or Q4 wrong: re-read “Total, marginal and average product” and Worked example 1 in the study guide. MP is a change; AP is a ratio.
- Q3 or Q6 wrong: re-read “How marginal product changes: three stages”. Diminishing returns begin where MP starts to fall, and they come from the fixed input.
- Q2 wrong: re-read “Short run and long run”.
- Q5 or Q7 incomplete: re-read “The three curves and how they are linked” and Figures 1 and 2.
Then tick off the topic checklist.