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. In every payoff matrix, cells show (row player’s payoff, column player’s payoff). Only addition, subtraction and multiplication are needed.
Question 1 (multiple choice · foundation)
Which combination of features best describes an oligopoly?
- (A) A few firms, decisions that depend on rivals’ reactions, and high barriers to entry
- (B) Many firms, differentiated products and low barriers to entry
- (C) One firm selling a product with no close substitutes
- (D) A few firms, each of which can ignore its rivals because its product is differentiated
Answer and explanation
Answer: (A). Few firms, interdependence and high barriers to entry are the defining features of oligopoly.
- (B) describes monopolistic competition, where each firm is too small for rivals to react to it.
- (C) describes monopoly: there are no rivals to be interdependent with.
- (D) gets the number of firms right but denies interdependence. Even with differentiated products, a few large firms must think about how rivals will respond.
Question 2 (multiple choice · core)
Two delivery apps, Pellow (row) and Zante (column), each decide whether to raise their delivery fee. Daily profits in $ thousand:
| Pellow ↓ / Zante → | Raise fee | Keep fee |
|---|---|---|
| Raise fee | (13, 11) | (6, 14) |
| Keep fee | (15, 7) | (9, 9) |
Which statement is correct?
- (A) Pellow’s dominant strategy is “raise fee”, because (Raise, Raise) gives the highest total profit.
- (B) Neither firm has a dominant strategy, because each firm’s profit depends on the other’s choice.
- (C) Zante’s dominant strategy is “raise fee”, because it earns 11 at (Raise, Raise) but only 9 at (Keep, Keep).
- (D) Both firms have the dominant strategy “keep fee”.
Answer and explanation
Answer: (D). Pellow: if Zante raises, keep 15 > raise 13; if Zante keeps, keep 9 > raise 6. Zante: if Pellow raises, keep 14 > raise 11; if Pellow keeps, keep 9 > raise 7. “Keep fee” wins every comparison for both firms.
- (A) uses the total payoff (24). A dominant strategy compares one player’s own payoffs, given each action of the other player.
- (B) confuses interdependence of payoffs with interdependence of the best choice. Profits depend on the rival’s choice, but the best action does not.
- (C) compares across the diagonal, changing Pellow’s action as well. Zante must compare its payoffs with Pellow’s action held fixed.
Question 3 (multiple choice · core)
Two bookshops, Arden (row) and Bexley (column), each decide whether to open on Sundays. Weekly profits in $ hundred:
| Arden ↓ / Bexley → | Open | Closed |
|---|---|---|
| Open | (32, 14) | (40, 18) |
| Closed | (26, 25) | (38, 21) |
What is the Nash equilibrium?
- (A) Arden opens, Bexley opens
- (B) Arden closes, Bexley closes
- (C) Arden opens, Bexley closes
- (D) There is none, because Bexley has no dominant strategy
Answer and explanation
Answer: (C). Arden’s dominant strategy is to open (32 > 26 and 40 > 38). Bexley has no dominant strategy, but its best response to Arden opening is to close (18 > 14). At (Open, Closed), neither shop can gain by changing alone: Arden would earn 38 instead of 40 by closing, and Bexley 14 instead of 18 by opening.
- (A) correctly uses Arden’s dominant strategy but assumes Bexley copies it. Given that Arden opens, Bexley earns more by closing (18 > 14).
- (B) is the cell with the highest total (59), but Arden would switch to opening (40 > 38) and so would Bexley (25 > 21).
- (D) is wrong because a Nash equilibrium does not need both players to have a dominant strategy.
Question 4 (multiple choice · core)
Which statement about oligopoly is correct?
- (A) Oligopolies always reach the monopoly outcome, because a small number of firms can easily agree.
- (B) Prices are usually higher and output lower than in perfect competition, even though cartels often break down.
- (C) In the long run, new firms enter until oligopolists earn zero economic profit.
- (D) Oligopoly is allocatively efficient because firms watch each other closely.
Answer and explanation
Answer: (B). Firms in oligopoly have market power, so even without a working cartel the price stays above marginal cost and output stays below the competitive level.
- (A) ignores the incentive to cheat: each cartel member gains by producing more, so the monopoly outcome is hard to sustain.
- (C) describes markets with low barriers to entry. High barriers let oligopoly profit last.
- (D) confuses interdependence with efficiency. Allocative efficiency needs P = MC, which oligopoly does not usually reach.
Question 5 (calculation · core)
Two airlines, Corra Air (row) and Velo Jet (column), fly the same route. Each chooses a high fare or a low fare. Daily profits in $ thousand:
| Corra ↓ / Velo → | High fare | Low fare |
|---|---|---|
| High fare | (90, 80) | (40, 100) |
| Low fare | (110, 45) | (65, 55) |
(a) Identify each airline’s dominant strategy, if any, with the comparisons that show it. (b) Identify the Nash equilibrium and explain why this game is a prisoner’s dilemma. (c) An airport loyalty scheme would pay Corra an extra amount R per day whenever it charges the high fare. Calculate the value that R must exceed for the high fare to become Corra’s dominant strategy. (d) If R = 30 and Velo’s payoffs are unchanged, find the new Nash equilibrium.
Model answer and suggested Marlbridge rubric
(a) Corra: if Velo charges high, low 110 > high 90; if Velo charges low, low 65 > high 40. Low fare is Corra’s dominant strategy. Velo: if Corra charges high, low 100 > high 80; if Corra charges low, low 55 > high 45. Low fare is Velo’s dominant strategy.
(b) The Nash equilibrium is (Low, Low) with (65, 55). It is a prisoner’s dilemma because both airlines would earn more at (High, High), with (90, 80), but each has a dominant strategy to charge the low fare.
(c) High must beat low in both columns:
- If Velo charges high: 90 + R > 110, so R > 20.
- If Velo charges low: 40 + R > 65, so R > 25.
R must exceed $25 thousand per day (the larger gap).
(d) With R = 30, Corra’s high-fare payoffs become 120 and 70. High is now Corra’s dominant strategy (120 > 110 and 70 > 65). Velo still prefers the low fare (100 > 80 and 55 > 45). The new Nash equilibrium is (High, Low) with (70, 100). The scheme changes Corra’s behaviour but does not bring about the cooperative (High, High) outcome, because Velo’s incentives are unchanged.
| Point | What earns it |
|---|---|
| 1 | Low fare dominant for both, with comparisons for each |
| 1 | Nash equilibrium (Low, Low) |
| 1 | Prisoner’s dilemma explained: both better off at (High, High) |
| 1 | R > 25, using both columns and choosing the larger gap |
| 1 | New equilibrium (High, Low) with a reason for each airline |
Do not award the fourth point for R > 20: that only makes the high fare better when Velo also charges high.
Question 6 (constructed response · core)
Two towns, Ferrin (row) and Gallo (column), share a lake. Each town decides whether to limit fishing or fish freely. The yearly value of the catch to each town, in $ thousand:
| Ferrin ↓ / Gallo → | Limit | Fish freely |
|---|---|---|
| Limit | (200, 200) | (120, 260) |
| Fish freely | (260, 120) | (150, 150) |
(a) Find each town’s dominant strategy and the Nash equilibrium. (b) Explain why the towns end up worse off than they could be. (c) A regional authority will fine any town that fishes freely an amount F per year. Calculate the value F must exceed for “limit” to become each town’s dominant strategy, and state the new Nash equilibrium. (d) Explain how this game is similar to the problem facing a cartel.
Model answer and suggested Marlbridge rubric
(a) Ferrin: if Gallo limits, fish freely 260 > limit 200; if Gallo fishes freely, 150 > 120. Fishing freely is dominant. The game is symmetric, so fishing freely is also Gallo’s dominant strategy. Nash equilibrium: (Fish freely, Fish freely) with (150, 150).
(b) Each town gains by fishing freely whatever the other does, so both do. But (Limit, Limit) gives 200 each, more than 150 each. Acting in its own interest, each town makes both worse off: a prisoner’s dilemma.
(c) Limit must beat fishing freely in both columns:
- If the other town limits: 200 > 260 − F, so F > 60.
- If the other town fishes freely: 120 > 150 − F, so F > 30.
F must exceed $60 thousand per year. Then limit is dominant for both towns and the new Nash equilibrium is (Limit, Limit) with 200 each; no fine is actually paid.
(d) Like cartel members who agree to restrict output, both towns gain if they restrain themselves together. But each has an incentive to “cheat” (fish more, or produce more) when the other keeps to the agreement. Without enforcement, cooperation breaks down.
| Point | What earns it |
|---|---|
| 1 | Fish freely dominant for both, with comparisons, and the Nash equilibrium |
| 1 | Both better off at (Limit, Limit) but each has an incentive to fish freely |
| 1 | F > 60 from the larger of the two gaps |
| 1 | New equilibrium (Limit, Limit) |
| 1 | Clear link: incentive to cheat on a mutually beneficial agreement, as in a cartel |
Common error: answering F > 30. A fine of, say, $40 thousand would still leave a town better off fishing freely when the other limits (260 − 40 = 220 > 200).
Question 7 (explanation · stretch)
Only two firms, Marro and Nesta, produce salt on a fictional island. Market demand is P = 110 − Q (Q in thousand tonnes per week, P in $ per tonne). Each firm has a constant MC = ATC = $10 per tonne.
(a) Find the price and quantity if the market were perfectly competitive. (b) The firms form a cartel and act as a monopoly, splitting output equally. Find the market price, each firm’s quota and each firm’s profit. (MR = 110 − 2Q.) (c) Each firm can keep its quota or cheat by producing 30 thousand tonnes. Build the payoff matrix and find the Nash equilibrium. (d) Compare the equilibrium in (c) with your answers to (a) and (b), and comment on efficiency.
Model answer and suggested Marlbridge rubric
(a) P = MC = $10; 110 − Q = 10, so Q = 100 thousand tonnes.
(b) MR = MC: 110 − 2Q = 10, so Q = 50 and P = 110 − 50 = $60. Quota = 25 thousand tonnes each. Profit each = (60 − 10) × 25 = $1,250 thousand per week (joint $2,500 thousand).
(c) Profit = (P − 10) × own output.
- Both keep: Q = 50, P = $60: 1,250 each.
- One cheats: Q = 55, P = $55: cheater 45 × 30 = 1,350; loyal firm 45 × 25 = 1,125.
- Both cheat: Q = 60, P = $50: 40 × 30 = 1,200 each.
| Marro ↓ / Nesta → | Keep quota | Cheat |
|---|---|---|
| Keep quota | (1,250, 1,250) | (1,125, 1,350) |
| Cheat | (1,350, 1,125) | (1,200, 1,200) |
Cheating is dominant for each firm (1,350 > 1,250 and 1,200 > 1,125). Nash equilibrium: (Cheat, Cheat), 1,200 each.
(d) At the equilibrium, Q = 60 and P = $50. Output is higher and price lower than under the cartel (50, $60), because the cartel breaks down. But price is still well above the competitive $10 and output below 100. Since P > MC, the market is allocatively inefficient, with a deadweight loss.
| Point | What earns it |
|---|---|
| 1 | Competitive P = $10 and Q = 100 |
| 1 | Cartel P = $60, quota 25 and profit 1,250 each |
| 1 | All four cells of the matrix correct |
| 1 | Cheat dominant for both and Nash equilibrium (Cheat, Cheat) |
| 1 | Equilibrium lies between cartel and competition, with P > MC stated as inefficient |
Accept a correct matrix shown in $ (for example 1,250,000) if the unit is clear.
How did you do?
- Q1 or Q4 wrong: re-read “What makes a market an oligopoly” and “Why oligopolists rarely reach the monopoly outcome” in the study guide.
- Q2 or Q3 wrong: re-read “A method that always works” and Worked example 2. Compare one player’s payoffs at a time.
- Q5(c) or Q6(c) wrong: re-read Worked example 1(c). Check every column and close the largest gap.
- Q7 incomplete: re-read “Collusion and cartels” and Figure 1.
Then tick off the topic checklist.