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, places and data are fictional. Unless a question says otherwise, every labour and capital market here is perfectly competitive. Only the four operations are needed.
Question 1 (multiple choice · foundation)
Corran Orchard sells apples in a perfectly competitive market at $5 per crate. With 3 pickers it harvests 220 crates per day; with 4 pickers it harvests 260 crates per day. What is the marginal revenue product of the 4th picker?
- (A) $40 per day
- (B) $200 per day
- (C) $325 per day
- (D) $1,300 per day
Answer and explanation
Answer: (B). MP of the 4th picker = 260 − 220 = 40 crates. MRP = MP × MR = 40 × $5 = $200 per day (MR = P because the orchard is a price taker).
- (A) is the marginal product in crates, not converted into dollars.
- (C) is the average revenue product: 260 × 5 ÷ 4 = $325. The hiring decision uses the marginal value.
- (D) is total revenue with 4 pickers (260 × 5), a level rather than a change.
Question 2 (multiple choice · core)
A small hotel hires cleaners in a perfectly competitive labour market. Which statement describes the labour supply curve the hotel faces?
- (A) It slopes upward, because the hotel must raise the wage to attract each extra cleaner.
- (B) It is the same as the market supply curve of cleaners.
- (C) It is horizontal at the market wage, which is also the hotel’s marginal resource cost.
- (D) It is vertical, because the number of cleaners in the town is fixed.
Answer and explanation
Answer: (C). The hotel is a wage taker. It hires such a small share of the town’s cleaners that it can take on as many as it wants at the market wage. So each extra cleaner costs the same wage: MRC = W, and the hotel’s supply curve is horizontal.
- (A) describes a monopsony (Topic 5.4), where one employer faces the whole upward-sloping market supply.
- (B) confuses the market with one firm. The market supply curve slopes upward; the single hotel faces only a horizontal line at the wage that curve helps set.
- (D) confuses short-run fixed numbers with what one small employer faces. Even if the town’s total were fixed, one hotel could still hire more at the going wage.
Question 3 (multiple choice · core)
A firm uses labour and capital. For the last units used, the marginal product of labour is 30 units and the wage is $15; the marginal product of capital is 50 units and the rental price of capital is $50. To produce its current output at the lowest cost, the firm should:
- (A) use more capital and less labour, because capital’s marginal product is higher.
- (B) use more labour and less capital, because labour adds more output per dollar.
- (C) use more of both inputs, because both marginal products are positive.
- (D) stop using capital altogether, because labour is cheaper.
Answer and explanation
Answer: (B). MP_L ÷ W = 30 ÷ 15 = 2 units per dollar. MP_K ÷ r = 50 ÷ 50 = 1 unit per dollar. Moving a dollar from capital to labour loses 1 unit and gains 2, so the same output can be made more cheaply. As the firm does this, MP_L falls and MP_K rises until the ratios are equal.
- (A) compares marginal products without dividing by the input prices.
- (C) is a question about how much to produce, which needs MRP and output prices; least cost is about the mix for a given output.
- (D) ignores diminishing returns: as more labour is used, MP_L falls, so the ratios meet before capital reaches zero.
Question 4 (multiple choice · core)
Seaborne Ferries is the only ferry operator on its route, so it faces a downward-sloping demand curve. It hires deckhands from a large, perfectly competitive regional labour market at $120 per day. Which statement is correct?
- (A) Seaborne must pay more than $120 because it is a monopoly.
- (B) Seaborne hires deckhands until the value of the marginal product (MP × P) equals $120.
- (C) Seaborne’s marginal resource cost rises with each deckhand it hires.
- (D) Seaborne hires deckhands until MRP equals $120, and its MRP is below MP × P.
Answer and explanation
Answer: (D). Seaborne has market power when it sells tickets but is a wage taker when it hires, so MRC = $120. It hires until MRP = $120. To sell more trips it must cut its price, so MR < P and MRP = MP × MR is less than VMP = MP × P.
- (A) mixes up output market power with labour market power. Seaborne is one of many employers of deckhands.
- (B) uses VMP, which overstates the revenue Seaborne gains, because it ignores the price cut on all trips.
- (C) describes a monopsony. A wage taker’s MRC is the constant market wage.
Question 5 (calculation · core)
Sunfield Car Wash sells car washes in a perfectly competitive market at $8 each. Other inputs are fixed.
| Workers | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Washes per day | 0 | 20 | 38 | 53 | 65 | 74 | 80 |
(a) Calculate MP and MRP for each worker. (b) The market wage is $96 per day. How many workers does Sunfield hire? Explain using the hiring rule. (c) The market wage rises to $120 per day. How many workers does Sunfield hire now? (d) The wage is back at $96, but the price of a wash rises to $12. How many workers does Sunfield hire?
Worked solution
(a)
| Worker | 1st | 2nd | 3rd | 4th | 5th | 6th |
|---|---|---|---|---|---|---|
| MP (washes) | 20 | 18 | 15 | 12 | 9 | 6 |
| MRP at $8 ($) | 160 | 144 | 120 | 96 | 72 | 48 |
(b) MRC = W = $96. Workers 1 to 3 have MRP above $96, and the 4th has MRP = $96 = W. The 5th has MRP $72 < $96. Sunfield hires 4 workers, where MRP = MRC = W.
(c) At $120, the 3rd worker’s MRP equals the wage and the 4th’s ($96) is below it. Sunfield hires 3 workers: a movement up along its MRP curve.
(d) New MRP = MP × $12: 240, 216, 180, 144, 108, 72. At W = $96, the 5th worker’s MRP ($108) is above the wage and the 6th’s ($72) is below. Sunfield hires 5 workers. A higher output price shifts the MRP curve to the right.
Suggested mark points (4): 1 for the MRP column; 1 for 4 workers with MRP = W; 1 for 3 workers; 1 for 5 workers with the new MRP values.
Common error: stopping at the 3rd worker in (b) because “MRP must be greater than the wage”. The 4th worker leaves profit unchanged; by convention the firm hires up to MRP = MRC.
Question 6 (graph · core)
The market for warehouse workers in the fictional city of Ashby is perfectly competitive, with a market wage of $18 per hour. Calder Logistics, one of hundreds of warehouse firms, hires 40 workers.
(a) Draw correctly labelled side-by-side graphs of the market for warehouse workers and of Calder Logistics. Show the market wage, Calder’s labour supply and MRC, its MRP curve and the 40 workers it hires. (b) Many warehouse workers move to another region. On your graphs, show the effect on the market wage and on the number of workers Calder hires. (c) Explain why Calder cannot keep paying $18 per hour after the change.
Model answer and suggested Marlbridge rubric
(a) Market graph: vertical axis “Wage ($ per hour)”, horizontal axis “Quantity of warehouse workers”; upward-sloping S and downward-sloping D cross at W₁ = $18. Firm graph: same vertical axis, horizontal axis “Number of workers (Calder)”; a horizontal line at $18 labelled S = MRC = W₁; a downward-sloping MRP (= D) curve crossing it at 40 workers.
(b) Market: supply shifts left (S₁ to S₂); the wage rises to W₂ above $18 and the market quantity falls. Firm: the horizontal line moves up to W₂ (new S = MRC). It crosses the unchanged MRP curve at fewer than 40 workers, so Calder hires fewer workers: a movement up along its MRP curve.
(c) Calder is a wage taker. If it paid below the new market wage, its workers could move to other warehouse firms paying W₂, and it could not hire anyone. So it must pay the market wage, and at that higher MRC fewer workers have MRP at least equal to the wage.
| Point | What earns it |
|---|---|
| 1 | Market graph correctly labelled with W₁ = $18 at the S and D intersection |
| 1 | Firm graph with a horizontal S = MRC at the market wage and a downward-sloping MRP, with 40 workers where they cross |
| 1 | Market supply shifts left and the wage rises |
| 1 | Firm’s wage line rises and Calder hires fewer than 40, read from the MRP curve |
| 1 | Explanation that a wage taker must pay the market wage because workers can move to other employers |
Do not award the fourth point if the MRP curve is shifted: the change affects labour supply, not Calder’s productivity or output price.
Question 7 (explanation · stretch)
Orrin Furniture sells chairs for $5 each in a perfectly competitive market. It pays W = $50 per worker per day and rents machines at r = $100 per machine per day.
| Units of input | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| MP of labour (chairs) | 25 | 20 | 15 | 10 | 8 | 5 |
| MP of capital (chairs) | 50 | 40 | 30 | 20 | 12 | 6 |
(a) Orrin uses 3 workers and 4 machines. Is it producing its output at the lowest possible cost? If not, which way should it change its input mix? (b) Find the profit-maximising number of workers and machines, and the daily cost of these inputs. (c) Show that both the least-cost rule and the profit-maximising rule hold at your answer to (b). (d) At 2 workers and 2 machines, the least-cost rule holds. Explain why this is not the profit-maximising choice.
Model answer and suggested Marlbridge rubric
(a) For the last units used: MP_L ÷ W = 15 ÷ 50 = 0.3 chairs per dollar; MP_K ÷ r = 20 ÷ 100 = 0.2 chairs per dollar. They are not equal, so not least cost. A dollar on labour adds more output, so Orrin should use more labour and fewer machines.
(b) MRP_L = MP_L × $5: 125, 100, 75, 50, 40, 25. MRP_L = W = $50 at the 4th worker; the 5th adds only $40. MRP_K = MP_K × $5: 250, 200, 150, 100, 60, 30. MRP_K = r = $100 at the 4th machine; the 5th adds only $60. Profit is maximised at 4 workers and 4 machines, costing 4 × 50 + 4 × 100 = $600 per day.
(c) Least cost: MP_L ÷ W = 10 ÷ 50 = 0.2 and MP_K ÷ r = 20 ÷ 100 = 0.2. Equal. ✓ Profit maximum: MRP_L ÷ W = 50 ÷ 50 = 1 and MRP_K ÷ r = 100 ÷ 100 = 1. ✓
(d) At 2 and 2, MP_L ÷ W = MP_K ÷ r = 0.4, so the mix is least-cost for that output. But MRP_L ÷ W = 100 ÷ 50 = 2 and MRP_K ÷ r = 200 ÷ 100 = 2. Each extra dollar on either input brings back $2 of revenue, so expanding both raises profit. Orrin is making the cheapest version of too little output.
| Point | What earns it |
|---|---|
| 1 | Both MP-per-dollar ratios at (3, 4) with the conclusion “more labour, fewer machines” |
| 1 | 4 workers and 4 machines using MRP = input price, with $600 |
| 1 | Both rules shown to hold at (4, 4) with numbers |
| 1 | Explanation that at (2, 2) MRP ÷ price is above 1, so least cost does not mean profit maximum |
Accept an answer to (a) that compares the ratios the other way (MP_K ÷ r < MP_L ÷ W) if the direction of change is correct.
How did you do?
- Q1 or Q5 wrong: re-read “The hiring rule” and Worked example 1 in the study guide. Convert MP to dollars first.
- Q2 or Q6 marked down: re-read “What makes a factor market perfectly competitive” and Figure 1. The firm’s supply line is horizontal at the market wage.
- Q4 wrong: re-read “MRP and VMP” and Worked example 2.
- Q3 or Q7 incomplete: re-read “Using more than one input” and Worked example 3.
Then tick off the topic checklist.