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. In every question, marginal cost is constant and there are no fixed costs unless stated, so MC = ATC and profit equals producer surplus. A four-function calculator is enough.
Question 1 (multiple choice · foundation)
Which of the following is not needed for a firm to practise price discrimination?
- (A) The firm faces a downward-sloping demand curve for its product.
- (B) The firm can identify buyers with different willingness to pay.
- (C) Buyers who pay a low price cannot easily resell to buyers charged a high price.
- (D) The firm’s marginal cost is the same at every level of output.
Answer and explanation
Answer: (D). Price discrimination needs market power, a way to separate buyers and a way to stop resale. The shape of the marginal cost curve does not matter; a firm with rising MC can still price discriminate.
- (A) is needed: a price taker cannot charge anyone more than the market price.
- (B) is needed: the firm must know whom to charge more.
- (C) is needed: otherwise low-price buyers would resell (arbitrage) and the high price would collapse.
Question 2 (multiple choice · core)
A single-price monopolist becomes able to practise perfect price discrimination. Compared with the single-price outcome, which is correct?
- (A) Output rises to the quantity where price equals marginal cost, consumer surplus falls to zero, and deadweight loss is eliminated.
- (B) Output falls, consumer surplus falls, and deadweight loss rises.
- (C) Output is unchanged, profit rises, and consumer surplus is unchanged.
- (D) Output rises, consumer surplus rises, and deadweight loss is eliminated.
Answer and explanation
Answer: (A). MR becomes the demand curve, so the firm produces where demand meets MC: the competitive quantity. Every buyer pays their maximum, so consumer surplus is zero, and no mutually beneficial unit is left unsold, so deadweight loss is zero.
- (B) describes the opposite of what happens to output and deadweight loss.
- (C) is wrong because output rises to where P = MC; profit does rise, but consumer surplus is captured by the firm.
- (D) gets output and deadweight loss right but consumer surplus wrong: the firm takes all of it.
Question 3 (multiple choice · core)
The only museum in a fictional city charges two groups separately. At current prices, visitors from overseas have a price elasticity of demand of 0.6 and local residents have a price elasticity of demand of 2.0 (both shown as positive numbers). Resale is impossible because tickets are checked against ID. To maximise profit, the museum should
- (A) charge local residents a higher price, because their demand is more elastic
- (B) charge overseas visitors a higher price, because their demand is less elastic
- (C) charge both groups the same price, because the cost of a visit is the same
- (D) charge overseas visitors a lower price, to attract more of them
Answer and explanation
Answer: (B). Overseas visitors’ demand is inelastic (0.6 < 1), so a higher price loses few of them. Local residents’ demand is elastic (2.0 > 1), so they get the lower price.
- (A) reverses the rule: the more elastic group pays the lower price.
- (C) ignores the point of price discrimination. Equal costs are exactly the case where a price difference counts as discrimination, and charging one price leaves profit unearned.
- (D) would cut the price where it gains the fewest extra visitors.
Question 4 (calculation · core)
Jonah is the only piano tuner on a fictional island. Six clients each want one tuning this month. Their maximum willingness to pay is shown below. Each tuning costs Jonah $25 (travel and parts), and he has no fixed costs.
| Client | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|
| Maximum willingness to pay ($) | 80 | 70 | 60 | 50 | 40 | 30 |
(a) Jonah must charge one price to all clients and can only choose one of the six values in the table. Find the profit-maximising price, the number of tunings and his profit. (b) Calculate consumer surplus at that price. (c) Jonah now charges each client their maximum. Find the number of tunings, his profit and consumer surplus. (d) Calculate the deadweight loss of the single-price outcome.
Worked solution
(a) Profit at each single price = (price − 25) × number of clients willing to pay it.
| Price ($) | 80 | 70 | 60 | 50 | 40 | 30 |
|---|---|---|---|---|---|---|
| Tunings | 1 | 2 | 3 | 4 | 5 | 6 |
| Profit ($) | 55 | 90 | 105 | 100 | 75 | 30 |
Best single price: $60, with 3 tunings and profit $105.
(b) U gains 80 − 60 = 20 and V gains 70 − 60 = 10; W gains 0. Consumer surplus = $30.
(c) Every client values a tuning above its $25 cost, so all 6 are served. Revenue = 80 + 70 + 60 + 50 + 40 + 30 = $330. Cost = 6 × 25 = $150. Profit = $180. Consumer surplus = $0.
(d) Under the single price, X, Y and Z are not served even though they value a tuning above $25. Lost surplus = (50 − 25) + (40 − 25) + (30 − 25) = 25 + 15 + 5 = $45. Check: total surplus with perfect price discrimination is $180; with one price it is 105 + 30 = $135; 180 − 135 = 45.
Suggested mark points (4): 1 for $60, 3 tunings and $105; 1 for CS = $30; 1 for 6 tunings and $180 with CS = 0; 1 for DWL = $45.
Common error: in (c), counting client Z as unprofitable. Z pays $30, which is more than the $25 cost, so serving Z adds $5 profit.
Question 5 (graph · core)
Pellow Gorge Zipline is the only zipline in a fictional national park. Demand is P = 80 − Q, where P is dollars per ride and Q is rides per day. Marginal cost is constant at $20 per ride.
(a) Draw a correctly labelled graph for the firm as a single-price monopolist. Show demand, MR and MC; label the profit-maximising quantity Qm and price Pm. Shade and label consumer surplus, profit and deadweight loss. (b) Calculate Qm, Pm, profit, consumer surplus and deadweight loss. (c) The firm starts perfect price discrimination. On a second graph, show the new quantity and the area that is now profit. (d) Calculate the new profit, consumer surplus and deadweight loss.
Model answer and suggested Marlbridge rubric
(a) Vertical axis “Price ($ per ride)”, horizontal axis “Quantity (rides per day)”. Demand from 80 on the price axis to 80 on the quantity axis. MR from 80 on the price axis to 40 on the quantity axis (twice as steep). MC horizontal at 20. Qm where MR crosses MC; Pm read up to demand. Consumer surplus: triangle above Pm, below demand. Profit: rectangle between Pm and MC from 0 to Qm. Deadweight loss: triangle between demand and MC from Qm to where demand meets MC.
(b) MR = 80 − 2Q = 20 gives Qm = 30 rides. Pm = 80 − 30 = $50. Profit = (50 − 20) × 30 = $900. CS = ½ × 30 × (80 − 50) = $450. Demand meets MC at 80 − Q = 20, so Q = 60. DWL = ½ × (60 − 30) × (50 − 20) = $450.
(c) Demand is now also the MR curve. Quantity is where demand meets MC: 60 rides. Shade the whole triangle under demand and above MC from 0 to 60 as profit.
(d) Profit = ½ × 60 × (80 − 20) = $1,800. CS = $0. DWL = $0.
| Point | What earns it |
|---|---|
| 1 | Correctly labelled axes, demand, MR below demand with the correct intercept, and MC |
| 1 | Qm at MR = MC and Pm read from demand (not MR), shown on the graph |
| 1 | CS, profit and DWL areas correctly placed and labelled |
| 1 | All five values in (b) correct |
| 1 | Perfect price discrimination graph: quantity at demand = MC, profit = whole triangle |
| 1 | Profit $1,800 with CS and DWL both zero |
Do not award the second point if Pm is read from the MR curve (that would give $20, not $50).
Question 6 (calculation · core)
Glenmore Cinema is the only cinema in a fictional town. Adults and students are separate markets; students must show a card. Q is in hundreds of tickets per week and P in dollars per ticket. MC is constant at $4 per ticket.
- Adult demand: P = 24 − Q
- Student demand: P = 12 − 0.5Q
(a) Find the profit-maximising price and quantity in each market, and total profit. (b) Calculate the price elasticity of demand for each group at the price chosen, and explain the price difference. (c) If the cinema must charge one price, it sets $10 and sells 18 hundred tickets. Show this is consistent with the two demand curves and calculate profit. By how much does price discrimination raise profit?
Worked solution
(a)
| Adults | Students | |
|---|---|---|
| MR | 24 − 2Q | 12 − Q |
| MR = MC | 24 − 2Q = 4, Q = 10 | 12 − Q = 4, Q = 8 |
| Price | 24 − 10 = $14 | 12 − 4 = $8 |
| Profit (hundreds of $) | (14 − 4) × 10 = 100 | (8 − 4) × 8 = 32 |
Total profit = 132 hundred dollars = $13,200 per week.
(b) Rewrite each demand as Q in terms of P. Adults: Q = 24 − P, so ΔQ ÷ ΔP = 1. Students: Q = 24 − 2P, so ΔQ ÷ ΔP = 2.
- Adults: 1 × (14 ÷ 10) = 1.4
- Students: 2 × (8 ÷ 8) = 2.0
Students’ demand is more elastic, so they are charged less. Adults are less sensitive to price, so the cinema charges them more.
(c) At $10, adults buy 24 − 10 = 14 and students buy 24 − 20 = 4: total 18 hundred tickets. Profit = (10 − 4) × 18 = 108 hundred = $10,800. Price discrimination raises profit by 13,200 − 10,800 = $2,400 per week.
| Point | What earns it |
|---|---|
| 1 | Correct MR for both groups and MR = MC used in each |
| 1 | Both prices read from demand: $14 and $8 |
| 1 | Total profit $13,200 (or 132 hundred) |
| 1 | Elasticities 1.4 and 2.0, with the less elastic group paying more |
| 1 | Single-price quantities 14 + 4 = 18, profit $10,800 and the $2,400 difference |
Accept elasticities calculated by another valid method if the conclusion (adults less elastic) is correct.
Question 7 (explanation · stretch)
A water-taxi company is the only way to reach a fictional island. A local newspaper writes: “The company now charges every passenger the most they are willing to pay. Economists call this efficient, so passengers must be better off.”
(a) Explain why perfect price discrimination is allocatively efficient. (b) Evaluate the claim that passengers must be better off. Refer to consumer surplus and to passengers who did not travel before. (c) Give two reasons why perfect price discrimination is hard to achieve in practice.
Model answer and suggested Marlbridge rubric
(a) Each extra trip earns exactly the price that passenger pays, so MR equals demand. The firm carries passengers until the last one’s willingness to pay equals marginal cost (P = MC). Every trip worth more to a passenger than it costs is made, so there is no deadweight loss and total surplus is maximised.
(b) The claim is mostly wrong. Efficiency is about the size of total surplus, not who receives it. Under perfect price discrimination every passenger pays their maximum, so consumer surplus is zero; the firm keeps all of it as profit. Passengers who used to pay the single price and valued the trip above it lose their consumer surplus. Passengers who valued a trip between MC and the old single price can now travel, but they pay their full value, so they gain no surplus either; they are no worse off, and the gain from their trips goes to the firm.
(c) Any two: the firm cannot know each passenger’s exact maximum willingness to pay; passengers have an incentive to hide or understate it; checking and setting individual prices is costly; preventing resale or transfer of tickets may be difficult.
| Point | What earns it |
|---|---|
| 1 | Last unit where P = MC (MR = demand), so no deadweight loss |
| 1 | Distinguishes efficiency (total surplus) from distribution (who gets it) |
| 1 | Consumer surplus falls to zero; the firm captures it as profit |
| 1 | Two valid practical obstacles |
How did you do?
- Q1 or Q3 wrong: re-read “The three conditions” and “Who pays more” in the study guide.
- Q2, Q5 or Q7 marked down: re-read “Perfect price discrimination”, Figures 1 and 2 and Worked example 1.
- Q4 or Q6 wrong: work through Worked example 2 again, and check you read every price from demand, not MR.
Then tick off the topic checklist.